NEWTON'S SECOND LAW OF MOTION, F=MA; EULER'S OR NEWTON'S?
Ajay Sharma
2017-01-01
Objective: F =ma is taught as Newton’s second law of motion all over the world. But it was given by Euler in 1775, forty-eight years after the death of Newton. It is debated here with scientific logic. Methods/Statistical analysis: The discussion partially deals with history of science so various aspects are quoted from original references. Newton did not give any equation in the Principia for second, third laws motion and law of gravitation. Conceptually, in Newton’s time, neither accele...
Newton's Laws, Euler's Laws and the Speed of Light
Whitaker, Stephen
2009-01-01
Chemical engineering students begin their studies of mechanics in a department of physics where they are introduced to the mechanics of Newton. The approach presented by physicists differs in both perspective and substance from that encountered in chemical engineering courses where Euler's laws provide the foundation for studies of fluid and solid…
Newton`s iteration for inversion of Cauchy-like and other structured matrices
Energy Technology Data Exchange (ETDEWEB)
Pan, V.Y. [Lehman College, Bronx, NY (United States); Zheng, Ailong; Huang, Xiaohan; Dias, O. [CUNY, New York, NY (United States)
1996-12-31
We specify some initial assumptions that guarantee rapid refinement of a rough initial approximation to the inverse of a Cauchy-like matrix, by mean of our new modification of Newton`s iteration, where the input, output, and all the auxiliary matrices are represented with their short generators defined by the associated scaling operators. The computations are performed fast since they are confined to operations with short generators of the given and computed matrices. Because of the known correlations among various structured matrices, the algorithm is immediately extended to rapid refinement of rough initial approximations to the inverses of Vandermonde-like, Chebyshev-Vandermonde-like and Toeplitz-like matrices, where again, the computations are confined to operations with short generators of the involved matrices.
Sparse contrast-source inversion using linear-shrinkage-enhanced inexact Newton method
Desmal, Abdulla
2014-07-01
A contrast-source inversion scheme is proposed for microwave imaging of domains with sparse content. The scheme uses inexact Newton and linear shrinkage methods to account for the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem, respectively. Thresholded shrinkage iterations are accelerated using a preconditioning technique. Additionally, during Newton iterations, the weight of the penalty term is reduced consistently with the quadratic convergence of the Newton method to increase accuracy and efficiency. Numerical results demonstrate the applicability of the proposed method.
Sparse contrast-source inversion using linear-shrinkage-enhanced inexact Newton method
Desmal, Abdulla; Bagci, Hakan
2014-01-01
A contrast-source inversion scheme is proposed for microwave imaging of domains with sparse content. The scheme uses inexact Newton and linear shrinkage methods to account for the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem, respectively. Thresholded shrinkage iterations are accelerated using a preconditioning technique. Additionally, during Newton iterations, the weight of the penalty term is reduced consistently with the quadratic convergence of the Newton method to increase accuracy and efficiency. Numerical results demonstrate the applicability of the proposed method.
High effective inverse dynamics modelling for dual-arm robot
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.
3D CSEM data inversion using Newton and Halley class methods
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
Newton-Krylov-Schwarz methods in unstructured grid Euler flow
Energy Technology Data Exchange (ETDEWEB)
Keyes, D.E. [Old Dominion Univ., Norfolk, VA (United States)
1996-12-31
Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton`s method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on an aerodynamic application emphasizing comparisons with a standard defect-correction approach and subdomain preconditioner consistency.
Experimental tests of the gravitational inverse-square law for mass separations from 2 to 105 cm
International Nuclear Information System (INIS)
Hoskins, J.K.; Newman, R.D.; Spero, R.; Schultz, J.
1985-01-01
We report two experiments which test the inverse-square distance dependence of the Newtonian gravitational force law. One experiment uses a torsion balance consisting of a 60-cm-long copper bar suspended at its midpoint by a tungsten wire, to compare the torque produced by copper masses 105 cm from the balance axis with the torque produced by a copper mass 5 cm from the side of the balance bar, near its end. Defining R/sub expt/ to be the measured ratio of the torques due to the masses at 105 cm and 5 cm, and R/sub Newton/ to be the corresponding ratio computed assuming an inverse-square force law, we find deltaequivalent(R/sub expt//R/sub Newton/-1) = (1.2 +- 7) x 10 -4 . Assuming a force deviating from an inverse-square distance dependence by a factor [1+epsilon lnr(cm)], this result implies epsilon = (0.5 +- 2.7) x 10 -4 . An earlier experiment, which has been reported previously, is described here in detail. This experiment tested the inverse-square law over a distance range of approximately 2 to 5 cm, by probing the gravitational field inside a steel mass tube using a copper test mass suspended from the end of a torsion balance bar. This experiment yielded a value for the parameter epsilon defined above: epsilon = (1 +- 7) x 10 -5 . The results of both of these experiments are in good agreement with the Newton- ian prediction. Limits on the strength and range of a Yukawa potential term superimposed on the Newtonian gravitational potential are discussed
Numerical solution of newton´s cooling differential equation by the methods of euler and runge-kutta
Directory of Open Access Journals (Sweden)
Andresa Pescador
2016-04-01
Full Text Available This article presents the first-order differential equations, which are a very important branch of mathematics as they have a wide applicability, in mathematics, as in physics, biology and economy. The objective of this study was to analyze the resolution of the equation that defines the cooling Newton's law. Verify its behavior using some applications that can be used in the classroom as an auxiliary instrument to the teacher in addressing these contents bringing answers to the questions of the students and motivating them to build their knowledge. It attempted to its resolution through two numerical methods, Euler method and Runge -Kutta method. Finally, there was a comparison of the approach of the solution given by the numerical solution with the analytical resolution whose solution is accurate.
Schroeder, Prosper
2007-01-01
La Philosophiae Naturalis Principia Mathematica de Newton (1686), marquait-elle le début d'une révolution scientifique, ou était-elle la simple synthèse des idées d'un Kepler, Galilée ou Hooke? Une analyse des idées de Newton écarte cette hypothèse par le simple fait que les Principia cherchaient à démontrer la fausseté des approches antérieures. Pourtant, Newton subit un échec dans l'application de sa théorie de la gravitation à l'explication du mouvement de la Lune, échec qui marqua le développement de la mécanique céleste pendant tout le 18e siècle. Clairaut, d'Alembert et Euler doutaient de la validité de la loi newtonienne presque en même temps et leurs idées firent progresser la mécanique céleste qui atteignit l'état de «science normale» avec Le traité de mécanique céleste de Laplace, un siècle après Newton. Cet ouvrage relate cet épisode de l'histoire des sciences exactes au 18e siècle et fournit un exemple des théories épistémologiques toujours en vigueur aujourd...
Time-domain incomplete Gauss-Newton full-waveform inversion of Gulf of Mexico data
AlTheyab, Abdullah; Wang, Xin; Schuster, Gerard T.
2013-01-01
We apply the incomplete Gauss-Newton full-waveform inversion (TDIGN-FWI) to Gulf of Mexico (GOM) data in the space-time domain. In our application, iterative least-squares reverse-time migration (LSRTM) is used to estimate the model update at each
Refinement of RAIM via Implementation of Implicit Euler Method
Energy Technology Data Exchange (ETDEWEB)
Lee, Yoonhee; Kim, Han-Chul [Korea Institute of Nuclear and Safety, Daejeon (Korea, Republic of)
2016-10-15
The first approach is a mechanistic approach which is used in LIRIC in which more than 200 reactions are modeled in detail. This approach enables to perform the detailed analysis. However, it requires huge computation burden. The other approach is a simplified model approach which is used in the IMOD, ASTEC/IODE, and etc. Recently, KINS has developed RAIM (Radio-Active Iodine chemistry Model) based on the simplified model approach. Since the numerical analysis module in RAIM is based on the explicit Euler method, there are major issues on the stability of the module. Therefore, implementation of a stable numerical method becomes essential. In this study, RAIM is refined via implementation of implicit Euler method in which the Newton method is used to find the solutions at each time step. The refined RAIM is tested by comparing to RAIM based on the explicit Euler method. In this paper, RAIM was refined by implementing the implicit Euler method. At each time step of the method in the refined RAIM, the reaction kinetics equations are solved by the Newton method in which elements of the Jacobian matrix are expressed analytically. With the results of OECD-BIP P10T2 test, the refined RAIM was compared to RAIM with the explicit Euler method. The refined RAIM shows better agreement with the experimental data than those from the explicit Euler method. For the rapid change of pH during the experiment, the refined RAIM gives more realistic changes in the concentrations of chemical species than those from the explicit Euler method. In addition, in terms of computing time, the refined RAIM shows comparable computing time to that with explicit Euler method. These comparisons are attributed to ⁓10 times larger time step size used in the implicit Euler method, even though computation burden at each time step in the refined RAIM is much higher than that of the explicit Euler method. Compared to the experimental data, the refined RAIM still shows discrepancy, which are attributed
Refinement of RAIM via Implementation of Implicit Euler Method
International Nuclear Information System (INIS)
Lee, Yoonhee; Kim, Han-Chul
2016-01-01
The first approach is a mechanistic approach which is used in LIRIC in which more than 200 reactions are modeled in detail. This approach enables to perform the detailed analysis. However, it requires huge computation burden. The other approach is a simplified model approach which is used in the IMOD, ASTEC/IODE, and etc. Recently, KINS has developed RAIM (Radio-Active Iodine chemistry Model) based on the simplified model approach. Since the numerical analysis module in RAIM is based on the explicit Euler method, there are major issues on the stability of the module. Therefore, implementation of a stable numerical method becomes essential. In this study, RAIM is refined via implementation of implicit Euler method in which the Newton method is used to find the solutions at each time step. The refined RAIM is tested by comparing to RAIM based on the explicit Euler method. In this paper, RAIM was refined by implementing the implicit Euler method. At each time step of the method in the refined RAIM, the reaction kinetics equations are solved by the Newton method in which elements of the Jacobian matrix are expressed analytically. With the results of OECD-BIP P10T2 test, the refined RAIM was compared to RAIM with the explicit Euler method. The refined RAIM shows better agreement with the experimental data than those from the explicit Euler method. For the rapid change of pH during the experiment, the refined RAIM gives more realistic changes in the concentrations of chemical species than those from the explicit Euler method. In addition, in terms of computing time, the refined RAIM shows comparable computing time to that with explicit Euler method. These comparisons are attributed to ⁓10 times larger time step size used in the implicit Euler method, even though computation burden at each time step in the refined RAIM is much higher than that of the explicit Euler method. Compared to the experimental data, the refined RAIM still shows discrepancy, which are attributed
Test of Newton's inverse-square law in the Greenland ice cap
International Nuclear Information System (INIS)
Ander, M.E.; Zumberge, M.A.; Lautzenhiser, T.
1989-01-01
An Airy-type geophysical experiment was conducted in a 2-km-deep hole in the Greenland ice cap at depths between 213 and 1673 m to test for possible violations of Newton's inverse-square law. An anomalous gravity gradient was observed. We cannot unambiguously attribute it to a breakdown of Newtonian gravity because we have shown that it might be due to unexpected geological features in the rock below the ice
The matrix Euler-Fermat theorem
International Nuclear Information System (INIS)
Arnol'd, Vladimir I
2004-01-01
We prove many congruences for binomial and multinomial coefficients as well as for the coefficients of the Girard-Newton formula in the theory of symmetric functions. These congruences also imply congruences (modulo powers of primes) for the traces of various powers of matrices with integer elements. We thus have an extension of the matrix Fermat theorem similar to Euler's extension of the numerical little Fermat theorem
A geometric feature of the Newton law of gravitation
Directory of Open Access Journals (Sweden)
Zhang Meirong
2017-06-01
Full Text Available In the Newton law of gravitation, the most miraculous fact is that the gravity is reciprocally proportional to the square of the distance between particles. In this paper, by assuming that the gravity is along with the line passing through particles and is proportional to the product of masses of particles, we will show that the above fact is equivalent to the geometric requirement that the gravity between two homogeneous balls is equal to that between two particles of the same masses located at the centers of balls. In fact, this will lead to a second-order Euler equation whose physical solution is reciprocally proportional to the square of the distance.
Directory of Open Access Journals (Sweden)
Lobes Herdiman
2012-01-01
Full Text Available Pengembangan komponen telapak tangan prosthetic terdiri dari metacarpal, metacarpal pollicis, dan jari tangan. Bahan yang digunakan yaitu nylon, jumlah komponen sebanyak 87 dan berat 175 gram. Kemampuan ibu jari dan jari telunjuk memegang peranan penting dalam melakukan 6 model gerakan. Posisi ujung phalanx media-distalis ibu jari dan jari telunjuk bertemu pada satu titik, sehingga mampu melakukan gerakan dasar tangan. Pengujian dengan eksperimen empiris pada pengembangan prosthetic tangan kosmetik dilakukan untuk mengetahui rotasi dari titik koordinat pada sendi pada saat aktivitas pemegangan. Sumbu koordinat ruang dan sistem dimana sumbu x, y, dan z, dengan titik nol ditetapkan pada pangkal poros utama. Model mekanisme prosthetic tangan kosmetik dengan sistem penarikan pada kendali kabel eksternal. Pengukuran tekanan pada ibu jari dengan jari telunjuk sebesar 493 gram yang dilakukan dengan alat dial indicator, pengukuran tekanan ibu jari dengan jari tengah sebesar 487 gram. Pengujian beban tarikan kabel untuk membuka jari menjadi terbuka penuh sebesar 4.291 gram dengan alat force gauge. Persamaan Newton-Euler menghasilkan besarnya torsi melalui persamaan forward (maju dan backward (mundur. Rotasi matriks yang disimbolkan xRx+1, dengan x adalah titik mulai dan x+1 adalah titik tujuan. Titik koordinat pada tiap ruas sebagai degree of freedom pada tiga titik, yaitu titik 0, titik 1, dan titik 2. Perhitungan matriks rotasi menggunakan titik awal (origin dan titik tujuan (destination. Titik 0 jari ditentukan pada sendi metacarpophalangeal, titik 1 pada sendi interphalangeal proximalis, dan titik 2 pada ujung komponen phalanx media-distalis sebagai end effector dimana ω0 = v0 = 0 dan gravitasi g = 9,8062 m/s2. Besarnya torsi maksimal dicapai pada gerakan spherical sebesar 10,00449 N.m, dengan mengkonversikan besaran torsi ke daya maka dicapai sebesar untuk gerakan spherical sebesar 12,5046 watt, dan daya terkecil pada gerakan lateral dan tip
Truncated Gauss-Newton Implementation for Multi-Parameter Full Waveform Inversion
Liu, Y.; Yang, J.; Dong, L.; Wang, Y.
2014-12-01
Full waveform inversion (FWI) is a numerical optimization method which aims at minimizing the difference between the synthetic and recorded seismic data to obtain high resolution subsurface images. A practical implementation for FWI is the adjoint-state method (AD), in which the data residuals at receiver locations are simultaneously back-propagated to form the gradient. Scattering-integral method (SI) is an alternative way which is based on the explicit building of the sensitivity kernel (Fréchet derivative matrix). Although it is more memory-consuming, SI is more efficient than AD when the number of the sources is larger than the number of the receivers. To improve the convergence of FWI, the information carried out by the inverse Hessian operator is crucial. Taking account accurately of the effect of this operator in FWI can correct illumination deficits, reserve the amplitude of the subsurface parameters, and remove artifacts generated by multiple reflections. In multi-parameter FWI, the off-diagonal blocks of the Hessian operator reflect the coupling between different parameter classes. Therefore, incorporating its inverse could help to mitigate the trade-off effects. In this study, we focus on the truncated Gauss-Newton implementation for multi-parameter FWI. The model update is computed through a matrix-free conjugate gradient solution of the Newton linear system. Both the gradient and the Hessian-vector product are calculated using the SI approach instead of the first- and second-order AD. However, the gradient expressed by kernel-vector product is calculated through the accumulation of the decomposed vector-scalar products. Thus, it's not necessary to store the huge sensitivity matrix beforehand. We call this method the matrix decomposition approach (MD). And the Hessian-vector product is replaced by two kernel-vector products which are then calculated by the above MD. By this way, we don't need to solve two additional wave propagation problems as in the
Directory of Open Access Journals (Sweden)
Claudio Estatico
2013-01-01
Full Text Available A microwave imaging method previously developed for tomographic inspection of dielectric targets is extended to three-dimensional objects. The approach is based on the full vector equations of the electromagnetic inverse scattering problem. The ill-posedness of the problem is faced by the application of an inexact-Newton method. Preliminary reconstruction results are reported.
A geophysical experiment on Newton's inverse-square law
International Nuclear Information System (INIS)
Achilli, V.; Errani, M.; Focardi, S.; Palmonari, F.; Pedrielli, F.
1997-01-01
A geophysical experiment consisting of measurement of the gravitational effect produced by a large water mass was performed in order to verify Newton's law. The use of a superconducting gravimeter lead to a precision of about 0.1 % in the final result. the ratio between the measured and the expected gravitational effect differs from 1 by more than 9 standard deviations. This may be explained by adding to the Newtonian potential a Yukawa repulsive term. The experimental result leads to constraints for the relationship between the relative magnitude (α) of the new term and the range (λ) of the interaction. In the region 20 m < λ < 500 m, α ranges from 2.6 % to 1.3 %
Time-domain incomplete Gauss-Newton full-waveform inversion of Gulf of Mexico data
AlTheyab, Abdullah
2013-09-22
We apply the incomplete Gauss-Newton full-waveform inversion (TDIGN-FWI) to Gulf of Mexico (GOM) data in the space-time domain. In our application, iterative least-squares reverse-time migration (LSRTM) is used to estimate the model update at each non-linear iteration, and the number of LSRTM iterations is progressively increased after each non-linear iteration. With this method, model updating along deep reflection wavepaths are automatically enhanced, which in turn improves imaging below the reach of diving-waves. The forward and adjoint operators are implemented in the space-time domain to simultaneously invert the data over a range of frequencies. A multiscale approach is used where higher frequencies are down-weighted significantly at early iterations, and gradually included in the inversion. Synthetic data results demonstrate the effectiveness of reconstructing both the high- and low-wavenumber features in the model without relying on diving waves in the inversion. Results with Gulf of Mexico field data show a significantly improved migration image in both the shallow and deep sections.
International Nuclear Information System (INIS)
Shan-Shan, Xu; Shu-Min, Li; Jamal, Berakdar
2009-01-01
As a counterexample of the Euler condition for nonholonomic constraint problems [H. C. Shen, Acta Phys. Sin. 54, 2468 (2005)], we investigate the Apell–Hamel dynamical system on a horizontally moving plate. The inconsistency of the results with Newton mechanics suggests that the Euler condition is not a universal model for nonlinear nonholonomic systems. This is attributed to the fact that the virtual displacements so obtained are not normal to the constraint forces. (general)
Is classical mechanics based on Newton's laws or Eulers analytical equations?
Directory of Open Access Journals (Sweden)
H.Iro
2005-01-01
Full Text Available In an example I illustrate how my picture of physics is enriched due to my frequent conversations with Reinhard Folk. The subject is: Who wrote down the basic equations of motion of classical mechanics for the first time? (To be sure, it was not Newton.
Iterative methods for compressible Navier-Stokes and Euler equations
Energy Technology Data Exchange (ETDEWEB)
Tang, W.P.; Forsyth, P.A.
1996-12-31
This workshop will focus on methods for solution of compressible Navier-Stokes and Euler equations. In particular, attention will be focused on the interaction between the methods used to solve the non-linear algebraic equations (e.g. full Newton or first order Jacobian) and the resulting large sparse systems. Various types of block and incomplete LU factorization will be discussed, as well as stability issues, and the use of Newton-Krylov methods. These techniques will be demonstrated on a variety of model transonic and supersonic airfoil problems. Applications to industrial CFD problems will also be presented. Experience with the use of C++ for solution of large scale problems will also be discussed. The format for this workshop will be four fifteen minute talks, followed by a roundtable discussion.
Sliding mode control of photoelectric tracking platform based on the inverse system method
Directory of Open Access Journals (Sweden)
Yao Zong Chen
2016-01-01
Full Text Available In order to improve the photoelectric tracking platform tracking performance, an integral sliding mode control strategy based on inverse system decoupling method is proposed. The electromechanical dynamic model is established based on multi-body system theory and Newton-Euler method. The coupled multi-input multi-output (MIMO nonlinear system is transformed into two pseudo-linear single-input single-output (SISO subsystems based on the inverse system method. An integral sliding mode control scheme is designed for the decoupled pseudo-linear system. In order to eliminate system chattering phenomenon caused by traditional sign function in sliding-mode controller, the sign function is replaced by the Sigmoid function. Simulation results show that the proposed decoupling method and the control strategy can restrain the influences of internal coupling and disturbance effectively, and has better robustness and higher tracking accuracy.
A new field experiment in the Greenland ice cap to test Newton's inverse square law
International Nuclear Information System (INIS)
Ander, M.E.; Nieto, M.M.; Zumberge, M.A.; Parker, R.L.; Lautzenhiser, T.; Aiken, C.L.V.; Ferguson, J.F.; McMechan, G.A.
1989-01-01
Recent experimental evidence suggests that Newton's law of gravity may not be precise. There are modern theories of quantum gravity that, in their attempts to unify gravity with other forces of nature, predict non-Newtonian gravitational forces that could have ranges on the order of 10 2 --10 5 m. If they exist, these forces would be apparent as violations of Newton's inverse square law. A geophysical experiment was carried out to search for possible finite-range, non-Newtonian gravity over depths of 213--1673 m in the glacial ice of the Greenland ice cap. The principal reason for this choice of experimental site is that a hole drilled through the ice cap already existed and the uniformity of the ice eliminates one of the major sources of uncertainty arising in the first of earlier studies, namely, the heterogeneity of the rocks through which a mine shaft or drill hole passes. This paper presents observations made in the summer of 1987 at Dye 3, Greenland, in the 2033-m-deep borehole, which reached the basement rock
Mechanics and Newton-Cartan-like gravity on the Newton-Hooke space-time
International Nuclear Information System (INIS)
Tian Yu; Guo Hanying; Huang Chaoguang; Xu Zhan; Zhou Bin
2005-01-01
We focus on the dynamical aspects on Newton-Hooke space-time NH + mainly from the viewpoint of geometric contraction of the de Sitter spacetime with Beltrami metric. (The term spacetime is used to denote a space with non-degenerate metric, while the term space-time is used to denote a space with degenerate metric.) We first discuss the Newton-Hooke classical mechanics, especially the continuous medium mechanics, in this framework. Then, we establish a consistent theory of gravity on the Newton-Hooke space-time as a kind of Newton-Cartan-like theory, parallel to the Newton's gravity in the Galilei space-time. Finally, we give the Newton-Hooke invariant Schroedinger equation from the geometric contraction, where we can relate the conservative probability in some sense to the mass density in the Newton-Hooke continuous medium mechanics. Similar consideration may apply to the Newton-Hooke space-time NH - contracted from anti-de Sitter spacetime
Remarks on Heisenberg-Euler-type electrodynamics
Kruglov, S. I.
2017-05-01
We consider Heisenberg-Euler-type model of nonlinear electrodynamics with two parameters. Heisenberg-Euler electrodynamics is a particular case of this model. Corrections to Coulomb’s law at r →∞ are obtained and energy conditions are studied. The total electrostatic energy of charged particles is finite. The charged black hole solution in the framework of nonlinear electrodynamics is investigated. We find the asymptotic of the metric and mass functions at r →∞. Corrections to the Reissner-Nordström solution are obtained.
3D GIS spatial operation based on extended Euler operators
Xu, Hongbo; Lu, Guonian; Sheng, Yehua; Zhou, Liangchen; Guo, Fei; Shang, Zuoyan; Wang, Jing
2008-10-01
The implementation of 3 dimensions spatial operations, based on certain data structure, has a lack of universality and is not able to treat with non-manifold cases, at present. ISO/DIS 19107 standard just presents the definition of Boolean operators and set operators for topological relationship query, and OGC GeoXACML gives formal definitions for several set functions without implementation detail. Aiming at these problems, based mathematical foundation on cell complex theory, supported by non-manifold data structure and using relevant research in the field of non-manifold geometry modeling for reference, firstly, this paper according to non-manifold Euler-Poincaré formula constructs 6 extended Euler operators and inverse operators to carry out creating, updating and deleting 3D spatial elements, as well as several pairs of supplementary Euler operators to convenient for implementing advanced functions. Secondly, we change topological element operation sequence of Boolean operation and set operation as well as set functions defined in GeoXACML into combination of extended Euler operators, which separates the upper functions and lower data structure. Lastly, we develop underground 3D GIS prototype system, in which practicability and credibility of extended Euler operators faced to 3D GIS presented by this paper are validated.
Suisky, Dieter
2008-01-01
"Euler as Physicist" analyzes the exceptional role of Leonhard Euler (1707 - 1783) in the history of science and emphasizes especially his fundamental contributions to physics. Although Euler is famous as the leading mathematician of the 18th century, his contributions to physics are as important for their innovative methods and solutions. Several books are devoted to Euler as mathematician, but none to Euler as physicist, like in this book. Euler’s contributions to mechanics are rooted in his life-long plan presented in two volume treatise programmatically entitled "Mechanics or the science of motion analytically demonstrated". Published in 1736, Euler’s treatise indicates the turn over from the traditional geometric representation of mechanics to a new approach. In writing Mechanics Euler did the first step to put the plan and his completion into practice through 1760. It is of particular interest to study how Euler made immediate use of his mathematics for mechanics and coordinated his progress in math...
Notes about Newton's Law corrections in non-factorizable geometries
International Nuclear Information System (INIS)
Santos, Victor Pereira do Nascimento; Almeida, Carlos Alberto Santos de
2011-01-01
Full text: Consistency of String Theory demands the existence of additional dimensions. Since then it was argued that, in order to observe the usual four-dimensional gravity, such dimensions must be compactified in such a way that they can only observed at very short distances. Localized gravity is however an alternative to compactification of extra dimensions, since it requires only the dominance of the ground state of Kaluza-Klein(KK) decomposition of the metric fluctuations over the other modes, associated to the extra dimensions. These modes have an interesting consequence in our world, which is the violation of the four-dimensional Newton's law of gravitation: massive KK modes contributes positively to the potential, leading to corrections which (usually) decreases faster than the inverse of distance. Moreover, the spectrum may have a gap, which is associated to a naked singularity along the additional dimensions. Each extra dimension presents a different contribution to this mass spectrum, since it can be compactified or not. Most of the work presented in literature consists in consider these contributions simultaneously. Our proposal in this work is to study the corrections to Newton's law due to the extra dimension scenario, studying separately the influence of one compact dimension and a non-compact one on the mass spectrum of the graviton. (author)
On the inverse Magnus effect in free molecular flow
Weidman, Patrick D.; Herczynski, Andrzej
2004-02-01
A Newton-inspired particle interaction model is introduced to compute the sideways force on spinning projectiles translating through a rarefied gas. The simple model reproduces the inverse Magnus force on a sphere reported by Borg, Söderholm and Essén [Phys. Fluids 15, 736 (2003)] using probability theory. Further analyses given for cylinders and parallelepipeds of rectangular and regular polygon section point to a universal law for this class of geometric shapes: when the inverse Magnus force is steady, it is proportional to one-half the mass M of gas displaced by the body.
Introducing the Notion of Bare and Effective Mass via Newton's Second Law of Motion
Pinto, Marcus Benghi
2007-01-01
The concepts of bare and effective mass are widely used within modern physics. Their meaning is discussed in advanced undergraduate and graduate courses such as solid state physics, nuclear physics and quantum field theory. Here I discuss how these concepts may be introduced together with the discussion of Newton's second law of motion. The…
The Newton papers the strange and true odyssey of Isaac Newton's manuscripts
Dry, Sarah
2014-01-01
When Isaac Newton died at 85 without a will on March 20, 1727, he left a mass of disorganized papers-upwards of 8 million words-that presented an immediate challenge to his heirs. Most of these writings, on subjects ranging from secret alchemical formulas to impassioned rejections of the Holy Trinity to notes and calculations on his core discoveries in calculus, universal gravitation, and optics, were summarily dismissed by his heirs as "not fit to be printed." Rabidly heretical, alchemically obsessed, and possibly even mad, the Newton presented in these papers threatened to undermine not just his personal reputation but the status of science itself. As a result, the private papers of the world's greatest scientist remained hidden to all but a select few for over two hundred years. In The Newton Papers, Sarah Dry divulges the story of how this secret archive finally came to light-and the complex and contradictory man it revealed. Covering a broad swath of history, Dry explores who controlled Newton's legacy, ...
Smith, G. A.; Meyer, G.; Nordstrom, M.
1986-01-01
A new automatic flight control system concept suitable for aircraft with highly nonlinear aerodynamic and propulsion characteristics and which must operate over a wide flight envelope was investigated. This exact model follower inverts a complete nonlinear model of the aircraft as part of the feed-forward path. The inversion is accomplished by a Newton-Raphson trim of the model at each digital computer cycle time of 0.05 seconds. The combination of the inverse model and the actual aircraft in the feed-forward path alloys the translational and rotational regulators in the feedback path to be easily designed by linear methods. An explanation of the model inversion procedure is presented. An extensive set of simulation data for essentially the full flight envelope for a vertical attitude takeoff and landing aircraft (VATOL) is presented. These data demonstrate the successful, smooth, and precise control that can be achieved with this concept. The trajectory includes conventional flight from 200 to 900 ft/sec with path accelerations and decelerations, altitude changes of over 6000 ft and 2g and 3g turns. Vertical attitude maneuvering as a tail sitter along all axes is demonstrated. A transition trajectory from 200 ft/sec in conventional flight to stationary hover in the vertical attitude includes satisfactory operation through lift-cure slope reversal as attitude goes from horizontal to vertical at constant altitude. A vertical attitude takeoff from stationary hover to conventional flight is also demonstrated.
Dolinko, A. E.
2009-01-01
By simulating the dynamics of a bidimensional array of springs and masses, the propagation of conveniently generated waves is visualized. The simulation is exclusively based on Newton's second law and was made to provide insight into the physics of wave propagation. By controlling parameters such as the magnitude of the mass and the elastic…
Introducing the notion of bare and effective mass via Newton's second law of motion
International Nuclear Information System (INIS)
Pinto, Marcus Benghi
2007-01-01
The concepts of bare and effective mass are widely used within modern physics. Their meaning is discussed in advanced undergraduate and graduate courses such as solid state physics, nuclear physics and quantum field theory. Here I discuss how these concepts may be introduced together with the discussion of Newton's second law of motion. The setting up of simple equations for the effective mass will allow instructors to discuss how external parameters, such as the temperature, influence this quantity. By expressing this type of equation as a power series one may also discuss perturbation theory and introduce Feynman diagrams
Programming for the Newton software development with NewtonScript
McKeehan, Julie
1994-01-01
Programming for the Newton: Software Development with NewtonScript focuses on the processes, approaches, operations, and principles involved in software development with NewtonScript.The publication first elaborates on Newton application design, views on the Newton, and protos. Discussions focus on system protos, creating and using user protos, linking and naming templates, creating the views of WaiterHelper, Newton application designs, and life cycle of an application. The text then elaborates on the fundamentals of NewtonScript, inheritance in NewtonScript, and view system and messages. Topi
On deviations from Newton's law and the proposal for a 'Fifth Force'
International Nuclear Information System (INIS)
Ferreira, L.A.; Malbouisson, A.P.C.
1986-01-01
The results of geophysical and laboratory measurements of Newton's constant of gravitation, seem to disagree by one percent. Attempts to explain this have led to the revival of the proposal for a fifth interaction in Nature. The experimental results on measurements of G and tests of Newton's inverse square law are reviewed. The recent reanalysis of the Eoetvoes experiment and proposals for new experiments are discussed. (Author) [pt
Deviations from Newton's law in supersymmetric large extra dimensions
International Nuclear Information System (INIS)
Callin, P.; Burgess, C.P.
2006-01-01
Deviations from Newton's inverse-squared law at the micron length scale are smoking-gun signals for models containing supersymmetric large extra dimensions (SLEDs), which have been proposed as approaches for resolving the cosmological constant problem. Just like their non-supersymmetric counterparts, SLED models predict gravity to deviate from the inverse-square law because of the advent of new dimensions at sub-millimeter scales. However SLED models differ from their non-supersymmetric counterparts in three important ways: (i) the size of the extra dimensions is fixed by the observed value of the dark energy density, making it impossible to shorten the range over which new deviations from Newton's law must be seen; (ii) supersymmetry predicts there to be more fields in the extra dimensions than just gravity, implying different types of couplings to matter and the possibility of repulsive as well as attractive interactions; and (iii) the same mechanism which is purported to keep the cosmological constant naturally small also keeps the extra-dimensional moduli effectively massless, leading to deviations from general relativity in the far infrared of the scalar-tensor form. We here explore the deviations from Newton's law which are predicted over micron distances, and show the ways in which they differ and resemble those in the non-supersymmetric case
Directory of Open Access Journals (Sweden)
Patrick Piprek
2018-02-01
Full Text Available This paper presents an approach to model a ski jumper as a multi-body system for an optimal control application. The modeling is based on the constrained Newton-Euler-Equations. Within this paper the complete multi-body modeling methodology as well as the musculoskeletal modeling is considered. For the musculoskeletal modeling and its incorporation in the optimization model, we choose a nonlinear dynamic inversion control approach. This approach uses the muscle models as nonlinear reference models and links them to the ski jumper movement by a control law. This strategy yields a linearized input-output behavior, which makes the optimal control problem easier to solve. The resulting model of the ski jumper can then be used for trajectory optimization whose results are compared to literature jumps. Ultimately, this enables the jumper to get a very detailed feedback of the flight. To achieve the maximal jump length, exact positioning of his body with respect to the air can be displayed.
Gravitational mass and Newton's universal gravitational law under relativistic conditions
International Nuclear Information System (INIS)
Vayenas, Constantinos G; Grigoriou, Dimitrios; Fokas, Athanasios
2015-01-01
We discuss the predictions of Newton's universal gravitational law when using the gravitational, m g , rather than the rest masses, m o , of the attracting particles. According to the equivalence principle, the gravitational mass equals the inertial mass, m i , and the latter which can be directly computed from special relativity, is an increasing function of the Lorentz factor, γ, and thus of the particle velocity. We consider gravitationally bound rotating composite states, and we show that the ratio of the gravitational force for gravitationally bound rotational states to the force corresponding to low (γ ≈ 1) particle velocities is of the order of (m Pl /m o ) 2 where mpi is the Planck mass (ħc/G) 1/2 . We also obtain a similar result, within a factor of two, by employing the derivative of the effective potential of the Schwarzschild geodesics of GR. Finally, we show that for certain macroscopic systems, such as the perihelion precession of planets, the predictions of this relativistic Newtonian gravitational law differ again by only a factor of two from the predictions of GR. (paper)
A comparison of different quasi-newton acceleration methods for partitioned multi-physics codes
CSIR Research Space (South Africa)
Haelterman, R
2018-02-01
Full Text Available & structures, 88/7, pp. 446–457 (2010) 8. J.E. Dennis, J.J. More´, Quasi-Newton methods: motivation and theory. SIAM Rev. 19, pp. 46–89 (1977) A Comparison of Quasi-Newton Acceleration Methods 15 9. J.E. Dennis, R.B. Schnabel, Least Change Secant Updates... Dois Metodos de Broyden. Mat. Apl. Comput. 1/2, pp. 135– 143 (1982) 25. J.M. Martinez, A quasi-Newton method with modification of one column per iteration. Com- puting 33, pp. 353–362 (1984) 26. J.M. Martinez, M.C. Zambaldi, An Inverse Column...
Numerical Tribute to Achievement of Euler
Figueroa-Navarro, Carlos; Molinar-Tabares, Martín Eduardo; Castro-Arce, Lamberto; Campos-García, Julio Cesar
2014-03-01
This work aims to make a tribute to one of the world's brightest personalities as it was the mathematical physicist Leonhard Euler (1707-1783). Some results where the influence of Euler persists with the novelty of applying numerical analysis using Matlab are here exposed. A first analysis was done with the series that defines Euler numbers and polynomials of Frobenius-Euler; another result is the characterization of the functions that carry to Euler-Macheroni constant. In hydrodynamics is also feasible to evaluate graphically the relationship between dimensions in diameter and the exit angle of the height of Euler for turbomachines. In differential equations of Cauchy-Euler solutions for the cases of distinct real roots and complex roots are generated. Furthermore we report the generation of the Fourier series and the Fourier transform calculated by using Direct Commands of Matlab. In variational calculus it is possible to obtain plots from a problem of the Euler Lagrange equations. Finally, the Euler function is analyzed. Our purpose is to present a tribute to this giant of science also it could be an excuse to study his legacy by utilizing modern computational techniques.
Advanced mechanics from Euler's determinism to Arnold's chaos
Rajeev, S G
2013-01-01
Classical Mechanics is the oldest and best understood part of physics. This does not mean that it is cast in marble yet, a museum piece to be admired from a distance. Instead, mechanics continues to be an active area of research by physicists and mathematicians. Every few years, we need to re-evaluate the purpose of learning mechanics and look at old material in the light of modern developments. Once you have learned basic mechanics (Newton's laws, the solution of the Kepler problem) and quantum mechanics (the Schrodinger equation, hydrogen atom) it is time to go back and relearn classical mechanics in greater depth. It is the intent of this book to take you through the ancient (the original meaning of "classical") parts of the subject quickly: the ideas started by Euler and ending roughly with Poincare. We then take up the developments of twentieth century physics that have largely to do with chaos and discrete time evolution (the basis of numerical solutions).
Nuclear power history calculation for subcritical systems using Euler-MacLaurin formula
International Nuclear Information System (INIS)
Henrice Junior, Edson; Goncalves, Alessandro da Cruz
2013-01-01
This paper presents an efficient method for calculating the reactivity using inverse point kinetic equation for subcritical systems by applying the Euler-MacLaurin summation formula to calculate the nuclear power history. In accordance with the accuracy of the numerical results, this method does not require a large number of points for calculation, providing accurate results with low computational cost. (author)
The cooling, mass and radius of the neutron star in EXO 0748-676 in quiescence with XMM-Newton
Cheng, Zheng; Méndez, Mariano; Díaz-Trigo, María; Costantini, Elisa
2017-01-01
We analyse four XMM-Newton observations of the neutron-star low-mass X-ray binary EXO 0748-676 in quiescence. We fit the spectra with an absorbed neutron-star atmosphere model, without the need for a high-energy (power-law) component; with a 95 per cent confidence the power law contributes less than
Designing stellarator coils by a modified Newton method using FOCUS
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.
Quasi-Newton methods for the acceleration of multi-physics codes
CSIR Research Space (South Africa)
Haelterman, R
2017-08-01
Full Text Available .E. Dennis, J.J. More´, Quasi-Newton methods: motivation and theory. SIAM Rev. 19, pp. 46–89 (1977) [11] J.E. Dennis, R.B. Schnabel, Least Change Secant Updates for quasi- Newton methods. SIAM Rev. 21, pp. 443–459 (1979) [12] G. Dhondt, CalculiX CrunchiX USER...) [25] J.M. Martinez, M.C. Zambaldi, An Inverse Column-Updating Method for solving large-scale nonlinear systems of equations. Optim. Methods Softw. 1, pp. 129–140 (1992) [26] J.M. Martinez, On the convergence of the column-updating method. Comp. Appl...
Extending Newton's law from nonlocal-in-time kinetic energy
International Nuclear Information System (INIS)
Suykens, J.A.K.
2009-01-01
We study a new equation of motion derived from a context of classical Newtonian mechanics by replacing the kinetic energy with a form of nonlocal-in-time kinetic energy. It leads to a hypothetical extension of Newton's second law of motion. In a first stage the obtainable solution form is studied by considering an unknown value for the nonlocality time extent. This is done in relation to higher-order Euler-Lagrange equations and a Hamiltonian framework. In a second stage the free particle case and harmonic oscillator case are studied and compared with quantum mechanical results. For a free particle it is shown that the solution form is a superposition of the classical straight line motion and a Fourier series. We discuss the link with quanta interpretations made in Pais-Uhlenbeck oscillators. The discrete nature emerges from the continuous time setting through application of the least action principle. The harmonic oscillator case leads to energy levels that approximately correspond to the quantum harmonic oscillator levels. The solution to the extended Newton equation also admits a quantization of the nonlocality time extent, which is determined by the classical oscillator frequency. The extended equation suggests a new possible way for understanding the relationship between classical and quantum mechanics
Investigating a Possible New Heavyweight Champion for Stellar Mass Black Holes with XMM-Newton
Barnard, Robin
Using methods described below, we have identified a record-breaking black hole candidate (BHC) associated with a globular cluster inside the Andromeda Galaxy (M31). Our BHC, known as XBo 135, has an inferred mass of 50 solar masses, around 60% heavier than the current record holder. We have been granted a 33 hr observation with the XMM-Newton X-ray observatory that will allow us to test different scenarios for the formation of such a beast. We are asking for $55k to support one postdoc (R. Barnard) for 6 months, travel to a conference to share our results, and publication in ApJ. We have strong observational evidence for two classes of black hole (BH): stellar mass BHs that are formed in the death throes of the most massive stars, and supermassive BHs that live at the centers of most galaxies. Stellar mass BHs are 3-30 times more massive than the Sun, while supermassive black holes 1 E+6 times more massive still. It is unknown how such massive black holes are formed, although we suspect the existence of a class of intermediate mass black holes that bridge the two populations. Our target, XBo 135, is an X-ray binary (XB) system where a compact object (neutron star or black hole) accretes material from a co-orbiting donor star; mass transfer from the donor to the compact object results in a huge release of energy, extracted from the gravitational potential energy of the in-falling matter. The material forms an accretion disk that gets faster and hotter as it approaches the accretor, extracting energy >10 times more efficiently than nuclear fusion. We have invented a method for identifying BHXBs from the X-ray emission alone, summarized as follows. At low accretion rates, all XBs exhibit strikingly similar emission that is dominated by a power law component with photon index 90% of the X-ray flux. Crucially, this emission is limited to luminosities below 10% of the Eddington limit , which is proportional to the mass of the accretor. If we observe low state emission at
Anatomy of Higgs mass in supersymmetric inverse seesaw models
Energy Technology Data Exchange (ETDEWEB)
Chun, Eung Jin, E-mail: ejchun@kias.re.kr [Korea Institute for Advanced Study, Seoul 130-722 (Korea, Republic of); Mummidi, V. Suryanarayana, E-mail: soori9@cts.iisc.ernet.in [Centre for High Energy Physics, Indian Institute of Science, Bangalore 560012 (India); Vempati, Sudhir K., E-mail: vempati@cts.iisc.ernet.in [Centre for High Energy Physics, Indian Institute of Science, Bangalore 560012 (India)
2014-09-07
We compute the one loop corrections to the CP-even Higgs mass matrix in the supersymmetric inverse seesaw model to single out the different cases where the radiative corrections from the neutrino sector could become important. It is found that there could be a significant enhancement in the Higgs mass even for Dirac neutrino masses of O(30) GeV if the left-handed sneutrino soft mass is comparable or larger than the right-handed neutrino mass. In the case where right-handed neutrino masses are significantly larger than the supersymmetry breaking scale, the corrections can utmost account to an upward shift of 3 GeV. For very heavy multi TeV sneutrinos, the corrections replicate the stop corrections at 1-loop. We further show that general gauge mediation with inverse seesaw model naturally accommodates a 125 GeV Higgs with TeV scale stops.
Testing the gravitational inverse-square law
International Nuclear Information System (INIS)
Adelberger, Eric; Heckel, B.; Hoyle, C.D.
2005-01-01
If the universe contains more than three spatial dimensions, as many physicists believe, our current laws of gravity should break down at small distances. When Isaac Newton realized that the acceleration of the Moon as it orbited around the Earth could be related to the acceleration of an apple as it fell to the ground, it was the first time that two seemingly unrelated physical phenomena had been 'unified'. The quest to unify all the forces of nature is one that still keeps physicists busy today. Newton showed that the gravitational attraction between two point bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. Newton's theory, which assumes that the gravitational force acts instantaneously, remained essentially unchallenged for roughly two centuries until Einstein proposed the general theory of relativity in 1915. Einstein's radical new theory made gravity consistent with the two basic ideas of relativity: the world is 4D - the three directions of space combined with time - and no physical effect can travel faster than light. The theory of general relativity states that gravity is not a force in the usual sense but a consequence of the curvature of this space-time produced by mass or energy. However, in the limit of low velocities and weak gravitational fields, Einstein's theory still predicts that the gravitational force between two point objects obeys an inverse-square law. One of the outstanding challenges in physics is to finish what Newton started and achieve the ultimate 'grand unification' - to unify gravity with the other three fundamental forces (the electromagnetic force, and the strong and weak nuclear forces) into a single quantum theory. In string theory - one of the leading candidates for an ultimate theory - the fundamental entities of nature are 1D strings and higher-dimensional objects called 'branes', rather than the point-like particles we are familiar with. String
International Nuclear Information System (INIS)
Voznyuk, I; Litman, A; Tortel, H
2015-01-01
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. (paper)
Rubin, Karl
2014-01-01
One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980s in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic G
Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD
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.
Does the Newton's world model revive
International Nuclear Information System (INIS)
Meszaros, A.
1984-03-01
Newton's world model may have a physical meaning if the gravitation has small non-zero mass and if the observable part of the universe is the interior of a giant finite body. Both possibilities are allowed theoretically. (author)
Some results on inverse scattering
International Nuclear Information System (INIS)
Ramm, A.G.
2008-01-01
A review of some of the author's results in the area of inverse scattering is given. The following topics are discussed: (1) Property C and applications, (2) Stable inversion of fixed-energy 3D scattering data and its error estimate, (3) Inverse scattering with 'incomplete' data, (4) Inverse scattering for inhomogeneous Schroedinger equation, (5) Krein's inverse scattering method, (6) Invertibility of the steps in Gel'fand-Levitan, Marchenko, and Krein inversion methods, (7) The Newton-Sabatier and Cox-Thompson procedures are not inversion methods, (8) Resonances: existence, location, perturbation theory, (9) Born inversion as an ill-posed problem, (10) Inverse obstacle scattering with fixed-frequency data, (11) Inverse scattering with data at a fixed energy and a fixed incident direction, (12) Creating materials with a desired refraction coefficient and wave-focusing properties. (author)
International Nuclear Information System (INIS)
Fee, David; Izbekov, Pavel; Kim, Keehoon; Yokoo, Akihiko; Lopez, Taryn
2017-01-01
Eruption mass and mass flow rate are critical parameters for determining the aerial extent and hazard of volcanic emissions. Infrasound waveform inversion is a promising technique to quantify volcanic emissions. Although topography may substantially alter the infrasound waveform as it propagates, advances in wave propagation modeling and station coverage permit robust inversion of infrasound data from volcanic explosions. The inversion can estimate eruption mass flow rate and total eruption mass if the flow density is known. However, infrasound-based eruption flow rates and mass estimates have yet to be validated against independent measurements, and numerical modeling has only recently been applied to the inversion technique. Furthermore we present a robust full-waveform acoustic inversion method, and use it to calculate eruption flow rates and masses from 49 explosions from Sakurajima Volcano, Japan.
Inexact proximal Newton methods for self-concordant functions
DEFF Research Database (Denmark)
Li, Jinchao; Andersen, Martin Skovgaard; Vandenberghe, Lieven
2016-01-01
with an application to L1-regularized covariance selection, in which prior constraints on the sparsity pattern of the inverse covariance matrix are imposed. In the numerical experiments the proximal Newton steps are computed by an accelerated proximal gradient method, and multifrontal algorithms for positive definite...... matrices with chordal sparsity patterns are used to evaluate gradients and matrix-vector products with the Hessian of the smooth component of the objective....
Using Euler buckling springs for vibration isolation
Winterflood, J; Blair, D G
2002-01-01
Difficulties in obtaining ideal vertical vibration isolation with mechanical springs are identified as being due to the mass of the elastic element which is in turn due to its energy storage requirement. A new technique to minimize this energy is presented - being an Euler column undergoing elastic buckling. The design of a high performance vertical vibration isolation stage based on this technique is presented together with its measured performance.
Using Euler buckling springs for vibration isolation
International Nuclear Information System (INIS)
Winterflood, J; Barber, T; Blair, D G
2002-01-01
Difficulties in obtaining ideal vertical vibration isolation with mechanical springs are identified as being due to the mass of the elastic element which is in turn due to its energy storage requirement. A new technique to minimize this energy is presented - being an Euler column undergoing elastic buckling. The design of a high performance vertical vibration isolation stage based on this technique is presented together with its measured performance
Alquimia: Isaac Newton revisitado Alchemy: Isaac Newton Revisited
Directory of Open Access Journals (Sweden)
Reginaldo Carmello Corrêa de Moraes
1997-01-01
Full Text Available Nota sobre publicações recentes que revelam aspectos pouco conhecidos da biblioteca de Newton - os numerosos textos religiosos, místicos e herméticos. Os biógrafos de Newton resistiram muito até admitir que os escritos esotéricos fossem genuíno interesse do sábio e que tivessem importância para entender sua trajetória intelectual. As publicações aqui indicadas afirmam o contrário, seguindo trilha aberta por ensaio pioneiro de J. M. Keynes (1946.A note on recent books about an unexplored side of Newtons library: religious, mystical and hermetic texts. Newton's biographers had resisted so much to believe that esoteric writings were in Newtons field of interest. Even if they recognized that, they didn't believe those strange works were important elements to understand his intellectual trajectory. The studies we mention here are saying just the opposite thing, exploring the way opened by the pioneer essay of J. M. Keynes (1946.
Improved Quasi-Newton method via PSB update for solving systems of nonlinear equations
Mamat, Mustafa; Dauda, M. K.; Waziri, M. Y.; Ahmad, Fadhilah; Mohamad, Fatma Susilawati
2016-10-01
The Newton method has some shortcomings which includes computation of the Jacobian matrix which may be difficult or even impossible to compute and solving the Newton system in every iteration. Also, the common setback with some quasi-Newton methods is that they need to compute and store an n × n matrix at each iteration, this is computationally costly for large scale problems. To overcome such drawbacks, an improved Method for solving systems of nonlinear equations via PSB (Powell-Symmetric-Broyden) update is proposed. In the proposed method, the approximate Jacobian inverse Hk of PSB is updated and its efficiency has improved thereby require low memory storage, hence the main aim of this paper. The preliminary numerical results show that the proposed method is practically efficient when applied on some benchmark problems.
Energy Technology Data Exchange (ETDEWEB)
Maulina, Hervin; Santoso, Iman, E-mail: iman.santoso@ugm.ac.id; Subama, Emmistasega; Nurwantoro, Pekik; Abraha, Kamsul [DepartmenFisika, Universitas Gadjah Mada, Sekip Utara BLS 21 Yogyakarta (Indonesia); Rusydi, Andrivo [Physics Department, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore)
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 part of the dielectric constant values and coefficient of extinction drastically increases at 4.5 eV similar to that of extracted using known DL fitting. The increase is known due to the process of interband transition and the interaction between the electrons and electron-hole at M-points in the Brillouin zone of graphene.
Density reconstruction in multiparameter elastic full-waveform inversion
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.
Fractal aspects and convergence of Newton`s method
Energy Technology Data Exchange (ETDEWEB)
Drexler, M. [Oxford Univ. Computing Lab. (United Kingdom)
1996-12-31
Newton`s Method is a widely established iterative algorithm for solving non-linear systems. Its appeal lies in its great simplicity, easy generalization to multiple dimensions and a quadratic local convergence rate. Despite these features, little is known about its global behavior. In this paper, we will explain a seemingly random global convergence pattern using fractal concepts and show that the behavior of the residual is entirely explicable. We will also establish quantitative results for the convergence rates. Knowing the mechanism of fractal generation, we present a stabilization to the orthodox Newton method that remedies the fractal behavior and improves convergence.
A modelling of robot manipulator dynamics based on Newton-Euler's equations
International Nuclear Information System (INIS)
Sasaki, Shinobu
1990-09-01
In this paper is presented an algorithm for solving the inverse dynamics of robot manipulators. In comparison with the dynamical equations derived from the Lagrange's mechanics, the relations to be treated are of simple forms due to recursive expressions of relative link motions. A computer simulation for applying the algorithm to a six-link manipulator indicated that the present method might be most appropriate among the existing approaches from the viewpoint of computational efficiency. In particular, it is noted that the increase of the number of links has hardly great effect on the intricacy of calculation. (author)
Efficient Underwater RSS Value to Distance Inversion Using the Lambert Function
Directory of Open Access Journals (Sweden)
Majid Hosseini
2014-01-01
Full Text Available There are many applications for using wireless sensor networks (WSN in ocean science; however, identifying the exact location of a sensor by itself (localization is still a challenging problem, where global positioning system (GPS devices are not applicable underwater. Precise distance measurement between two sensors is a tool of localization and received signal strength (RSS, reflecting transmission loss (TL phenomena, is widely used in terrestrial WSNs for that matter. Underwater acoustic sensor networks have not been used (UASN, due to the complexity of the TL function. In this paper, we addressed these problems by expressing underwater TL via the Lambert W function, for accurate distance inversion by the Halley method, and compared this to Newton-Raphson inversion. Mathematical proof, MATLAB simulation, and real device implementation demonstrate the accuracy and efficiency of the proposed equation in distance calculation, with fewer iterations, computation stability for short and long distances, and remarkably short processing time. Then, the sensitivities of Lambert W function and Newton-Raphson inversion to alteration in TL were examined. The simulation results showed that Lambert W function is more stable to errors than Newton-Raphson inversion. Finally, with a likelihood method, it was shown that RSS is a practical tool for distance measurement in UASN.
A combined modification of Newton`s method for systems of nonlinear equations
Energy Technology Data Exchange (ETDEWEB)
Monteiro, M.T.; Fernandes, E.M.G.P. [Universidade do Minho, Braga (Portugal)
1996-12-31
To improve the performance of Newton`s method for the solution of systems of nonlinear equations a modification to the Newton iteration is implemented. The modified step is taken as a linear combination of Newton step and steepest descent directions. In the paper we describe how the coefficients of the combination can be generated to make effective use of the two component steps. Numerical results that show the usefulness of the combined modification are presented.
International Nuclear Information System (INIS)
Egorov, Yurii V
2013-01-01
We consider the classical problem on the tallest column which was posed by Euler in 1757. Bernoulli-Euler theory serves today as the basis for the design of high buildings. This problem is reduced to the problem of finding the potential for the Sturm-Liouville equation corresponding to the maximum of the first eigenvalue. The problem has been studied by many mathematicians but we give the first rigorous proof of the existence and uniqueness of the optimal column and we give new formulae which let us find it. Our method is based on a new approach consisting in the study of critical points of a related nonlinear functional. Bibliography: 6 titles.
Data inversion in coupled subsurface flow and geomechanics models
International Nuclear Information System (INIS)
Iglesias, Marco A; McLaughlin, Dennis
2012-01-01
We present an inverse modeling approach to estimate petrophysical and elastic properties of the subsurface. The aim is to use the fully coupled geomechanics-flow model of Girault et al (2011 Math. Models Methods Appl. Sci. 21 169–213) to jointly invert surface deformation and pressure data from wells. We use a functional-analytic framework to construct a forward operator (parameter-to-output map) that arises from the geomechanics-flow model of Girault et al. Then, we follow a deterministic approach to pose the inverse problem of finding parameter estimates from measurements of the output of the forward operator. We prove that this inverse problem is ill-posed in the sense of stability. The inverse problem is then regularized with the implementation of the Newton-conjugate gradient (CG) algorithm of Hanke (1997 Numer. Funct. Anal. Optim. 18 18–971). For a consistent application of the Newton-CG scheme, we establish the differentiability of the forward map and characterize the adjoint of its linearization. We provide assumptions under which the theory of Hanke ensures convergence and regularizing properties of the Newton-CG scheme. These properties are verified in our numerical experiments. In addition, our synthetic experiments display the capabilities of the proposed inverse approach to estimate parameters of the subsurface by means of data inversion. In particular, the added value of measurements of surface deformation in the estimation of absolute permeability is quantified with respect to the standard history matching approach of inverting production data with flow models. The proposed methodology can be potentially used to invert satellite geodetic data (e.g. InSAR and GPS) in combination with production data for optimal monitoring and characterization of the subsurface. (paper)
Application of the numerical Laplace transform inversion to neutron transport theory
International Nuclear Information System (INIS)
Ganapol, B.D.
1989-01-01
A numerical Laplace transform inversion is developed using the Hurwitz-Zweifel method of evaluating the Fourier cosine integral coupled with an Euler-Knopp transformation. The numerical inversion is then applied to problems in linear transport theory concerning slowing down, time-dependence and featuring the determination of the interior scalar flux solution to the one-group stationary transport equation in half-space geometry
International Nuclear Information System (INIS)
Dolinko, A E
2009-01-01
By simulating the dynamics of a bidimensional array of springs and masses, the propagation of conveniently generated waves is visualized. The simulation is exclusively based on Newton's second law and was made to provide insight into the physics of wave propagation. By controlling parameters such as the magnitude of the mass and the elastic constant of the mesh elements, it was possible to change the properties of the medium in order to observe the characteristic phenomena of wave mechanics, such as diffraction and interference. Finally, several examples of waves propagating in media with different configurations are presented, including the application of the simulation to the study of frequency response of a complex structure.
Newton's gift how Sir Isaac Newton unlocked the system of the world
Berlinski, David
2000-01-01
Sir Isaac Newton, creator of the first and perhaps most important scientific theory, is a giant of the scientific era. Despite this, he has remained inaccessible to most modern readers, indisputably great but undeniably remote. In this witty, engaging, and often moving examination of Newton's life, David Berlinski recovers the man behind the mathematical breakthroughs. The story carries the reader from Newton's unremarkable childhood to his awkward undergraduate days at Cambridge through the astonishing year in which, working alone, he laid the foundation for his system of the world, his Principia Mathematica, and to the subsequent monumental feuds that poisoned his soul and wearied his supporters. An edifying appreciation of Newton's greatest accomplishment, Newton's Gift is also a touching celebration of a transcendent man.
NLSE: Parameter-Based Inversion Algorithm
Sabbagh, Harold A.; Murphy, R. Kim; Sabbagh, Elias H.; Aldrin, John C.; Knopp, Jeremy S.
Chapter 11 introduced us to the notion of an inverse problem and gave us some examples of the value of this idea to the solution of realistic industrial problems. The basic inversion algorithm described in Chap. 11 was based upon the Gauss-Newton theory of nonlinear least-squares estimation and is called NLSE in this book. In this chapter we will develop the mathematical background of this theory more fully, because this algorithm will be the foundation of inverse methods and their applications during the remainder of this book. We hope, thereby, to introduce the reader to the application of sophisticated mathematical concepts to engineering practice without introducing excessive mathematical sophistication.
Forensic analysis of explosions: Inverse calculation of the charge mass
Voort, M.M. van der; Wees, R.M.M. van; Brouwer, S.D.; Jagt-Deutekom, M.J. van der; Verreault, J.
2015-01-01
Forensic analysis of explosions consists of determining the point of origin, the explosive substance involved, and the charge mass. Within the EU fP7 project Hyperion, TNO developed the Inverse Explosion Analysis (TNO-IEA) tool to estïmate the charge mass and point of origin based on observed damage
Inverse dynamic analysis of general n-link robot manipulators
International Nuclear Information System (INIS)
Yih, T.C.; Wang, T.Y.; Burks, B.L.; Babcock, S.M.
1996-01-01
In this paper, a generalized matrix approach is derived to analyze the dynamic forces and moments (torques) required by the joint actuators. This method is general enough to solve the problems of any n-link open-chain robot manipulators with joint combinations of R(revolute), P(prismatic), and S(spherical). On the other hand, the proposed matrix solution is applicable to both nonredundant and redundant robotic systems. The matrix notation is formulated based on the Newton-Euler equations under the condition of quasi-static equilibrium. The 4 x 4 homogeneous cylindrical coordinates-Bryant angles (C-B) notation is applied to model the robotic systems. Displacements, velocities, and accelerations of each joint and link center of gravity (CG) are calculated through kinematic analysis. The resultant external forces and moments exerted on the CG of each link are considered as known inputs. Subsequently, a 6n x 6n displacement coefficient matrix and a 6n x 1 external force/moment vector can be established. At last, the joint forces and moments needed for the joint actuators to control the robotic system are determined through matrix inversion. Numerical examples will be illustrated for the nonredundant industrial robots: Bendix AA/CNC (RRP/RRR) and Unimate 2000 spherical (SP/RRR) robots; and the redundant light duty utility arm (LDUA), modified LDUA, and tank waste retrieval manipulator system
Trinification, the hierarchy problem, and inverse seesaw neutrino masses
International Nuclear Information System (INIS)
Cauet, Christophe; Paes, Heinrich; Wiesenfeldt, Soeren
2011-01-01
In minimal trinification models light neutrino masses can be generated via a radiative seesaw mechanism, where the masses of the right-handed neutrinos originate from loops involving Higgs and fermion fields at the unification scale. This mechanism is absent in models aiming at solving or ameliorating the hierarchy problem, such as low-energy supersymmetry, since the large seesaw scale disappears. In this case, neutrino masses need to be generated via a TeV-scale mechanism. In this paper, we investigate an inverse seesaw mechanism and discuss some phenomenological consequences.
p-Euler equations and p-Navier-Stokes equations
Li, Lei; Liu, Jian-Guo
2018-04-01
We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.
Newton's apple Isaac Newton and the English scientific renaissance
Aughton, Peter
2003-01-01
In the aftermath of the English Civil War, the Restoration overturned England's medieval outlook and a new way of looking at the world allowed the genius of Isaac Newton (b. 1642) and his contemporaries to flourish. Newton had a long and eventful life apart from his scentific discoveries. He was born at the beginnings of the Civil War, his studies were disrupted by the twin disasters of the Great Plague and the Fire of London; a brilliant and enigmatic genius, Newton dabbled in alchemy, wrote over a million words on the Bible, quarrelled with his contemporaries and spent his last years as Master of the Royal Mint as well as President of the Royal Society. This book sets Newton's life and work against this dramatic intellectual rebirth; among his friends and contemporaries were Samuel Pepys, the colourful diarist, John Evelyn, the eccentric antiquarian, the astronomers Edmund Halley and John Flamsteed, and Christopher Wren, the greatest architect of his age. They were all instrumental in the founding of the Ro...
Equivariant analogues of the Euler characteristic and Macdonald type equations
Gusein-Zade, S. M.
2017-02-01
One of the simplest and, at the same time, most important invariants of a topological space is the Euler characteristic. A generalization of the notion of the Euler characteristic to the equivariant setting, that is, to spaces with an action of a group (say, finite) is far from unique. An equivariant analogue of the Euler characteristic can be defined as an element of the ring of representations of the group or as an element of the Burnside ring of the group. From physics came the notion of the orbifold Euler characteristic, and this was generalized to orbifold Euler characteristics of higher orders. The main property of the Euler characteristic (defined in terms of the cohomology with compact support) is its additivity. On some classes of spaces there are additive invariants other than the Euler characteristic, and they can be regarded as generalized Euler characteristics. For example, the class of a variety in the Grothendieck ring of complex quasi-projective varieties is a universal additive invariant on the class of complex quasi-projective varieties. Generalized analogues of the Euler characteristic can also be defined in the equivariant setting. There is a simple formula — the Macdonald equation — for the generating series of the Euler characteristics of the symmetric powers of a space: it is equal to the series (1-t)-1=1+t+t^2+\\cdots independent of the space, raised to a power equal to the Euler characteristic of the space itself. Equations of a similar kind for other invariants (`equivariant and generalized Euler characteristics') are called Macdonald type equations. This survey discusses different versions of the Euler characteristic in the equivariant setting and describes some of their properties and Macdonald type equations. Bibliography: 59 titles.
An experimental test of Newton's law of gravitation for small accelerations
International Nuclear Information System (INIS)
Schubert, Sven
2011-10-01
The experiment presented in this thesis has been designed to test Newton's law of gravitation in the limit of small accelerations caused by weak gravitational forces. It is located at DESY, Hamburg, and is a modification of an experiment that was carried out in Wuppertal, Germany, until 2002 in order to measure the gravitational constant G. The idea of testing Newton's law in the case of small accelerations emerged from the question whether the flat rotation curves of spiral galaxies can be traced back to Dark Matter or to a law of gravitation that deviates from Newton on cosmic scales like e.g. MOND (Modified Newtonian Dynamics). The core of this experiment is a microwave resonator which is formed by two spherical concave mirrors that are suspended as pendulums. Masses between 1 and 9 kg symmetrically change their distance to the mirrors from far to near positions. Due to the increased gravitational force the mirrors are pulled apart and the length of the resonator increases. This causes a shift of the resonance frequency which can be translated into a shift of the mirror distance. The small masses are sources of weak gravitational forces and cause accelerations on the mirrors of about 10 -10 m/s 2 . These forces are comparable to those between stars on cosmic scales and the accelerations are in the vicinity of the characteristic acceleration of MOND a 0 ∼ 1.2.10 -10 m/s 2 , where deviations from Newton's law are expected. Thus Newton's law could be directly checked for correctness under these conditions. First measurements show that due to the sensitivity of this experiment many systematic influences have to be accounted for in order to get consistent results. Newton's law has been confirmed with an accuracy of 3%. MOND has also been checked. In order to be able to distinguish Newton from MOND with other interpolation functions the accuracy of the experiment has to be improved. (orig.)
Isaac Newton: Eighteenth-century Perspectives
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
International Nuclear Information System (INIS)
Jin Qinian
2008-01-01
In this paper we consider the iteratively regularized Gauss–Newton method for solving nonlinear ill-posed inverse problems. Under merely the Lipschitz condition, we prove that this method together with an a posteriori stopping rule defines an order optimal regularization method if the solution is regular in some suitable sense
Newton law in DGP brane-world with semi-infinite extra dimension
International Nuclear Information System (INIS)
Park, D.K.; Tamaryan, S.; Miao Yangang
2004-01-01
Newton potential for DGP brane-world scenario is examined when the extra dimension is semi-infinite. The final form of the potential involves a self-adjoint extension parameter α, which plays a role of an additional mass (or distance) scale. The striking feature of Newton potential in this setup is that the potential behaves as seven-dimensional in long range when α is non-zero. For small α there is an intermediate range where the potential is five-dimensional. Five-dimensional Newton constant decreases with increase of α from zero. In the short range the four-dimensional behavior is recovered. The physical implication of this result is discussed in the context of the accelerating behavior of universe
Newton and scholastic philosophy.
Levitin, Dmitri
2016-03-01
This article examines Isaac Newton's engagement with scholastic natural philosophy. In doing so, it makes two major historiographical interventions. First of all, the recent claim that Newton's use of the concepts of analysis and synthesis was derived from the Aristotelian regressus tradition is challenged on the basis of bibliographical, palaeographical and intellectual evidence. Consequently, a new, contextual explanation is offered for Newton's use of these concepts. Second, it will be shown that some of Newton's most famous pronouncements - from the General Scholium appended to the second edition of the Principia (1713) and from elsewhere - are simply incomprehensible without an understanding of specific scholastic terminology and its later reception, and that this impacts in quite significant ways on how we understand Newton's natural philosophy more generally. Contrary to the recent historiographical near-consensus, Newton did not hold an elaborate metaphysics, and his seemingly 'metaphysical' statements were in fact anti-scholastic polemical salvoes. The whole investigation will permit us a brief reconsideration of the relationship between the self-proclaimed 'new' natural philosophy and its scholastic predecessors.
Lojasiewicz exponents and Newton polyhedra
International Nuclear Information System (INIS)
Pham Tien Son
2006-07-01
In this paper we obtain the exact value of the Lojasiewicz exponent at the origin of analytic map germs on K n (K = R or C under the Newton non-degeneracy condition, using information from their Newton polyhedra. We also give some conclusions on Newton non-degenerate analytic map germs. As a consequence, we obtain a link between Newton non-degenerate ideals and their integral closures, thus leading to a simple proof of a result of Saia. Similar results are also considered to polynomial maps which are Newton non-degenerate at infinity. (author)
Solution of the Cox-Thompson inverse scattering problem using finite set of phase shifts
Apagyi, B; Scheid, W
2003-01-01
A system of nonlinear equations is presented for the solution of the Cox-Thompson inverse scattering problem (1970 J. Math. Phys. 11 805) at fixed energy. From a given finite set of phase shifts for physical angular momenta, the nonlinear equations determine related sets of asymptotic normalization constants and nonphysical (shifted) angular momenta from which all quantities of interest, including the inversion potential itself, can be calculated. As a first application of the method we use input data consisting of a finite set of phase shifts calculated from Woods-Saxon and box potentials representing interactions with diffuse or sharp surfaces, respectively. The results for the inversion potentials, their first moments and asymptotic properties are compared with those provided by the Newton-Sabatier quantum inversion procedure. It is found that in order to achieve inversion potentials of similar quality, the Cox-Thompson method requires a smaller set of phase shifts than the Newton-Sabatier procedure.
Solution of the Cox-Thompson inverse scattering problem using finite set of phase shifts
International Nuclear Information System (INIS)
Apagyi, Barnabas; Harman, Zoltan; Scheid, Werner
2003-01-01
A system of nonlinear equations is presented for the solution of the Cox-Thompson inverse scattering problem (1970 J. Math. Phys. 11 805) at fixed energy. From a given finite set of phase shifts for physical angular momenta, the nonlinear equations determine related sets of asymptotic normalization constants and nonphysical (shifted) angular momenta from which all quantities of interest, including the inversion potential itself, can be calculated. As a first application of the method we use input data consisting of a finite set of phase shifts calculated from Woods-Saxon and box potentials representing interactions with diffuse or sharp surfaces, respectively. The results for the inversion potentials, their first moments and asymptotic properties are compared with those provided by the Newton-Sabatier quantum inversion procedure. It is found that in order to achieve inversion potentials of similar quality, the Cox-Thompson method requires a smaller set of phase shifts than the Newton-Sabatier procedure
Heat kernel for Newton-Cartan trace anomalies
Energy Technology Data Exchange (ETDEWEB)
Auzzi, Roberto [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via Musei 41, Brescia, 25121 (Italy); INFN Sezione di Perugia, Via A. Pascoli, Perugia, 06123 (Italy); Nardelli, Giuseppe [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via Musei 41, Brescia, 25121 (Italy); TIFPA - INFN, Università di Trento,c/o Dipartimento di Fisica, Povo, TN, 38123 (Italy)
2016-07-11
We compute the leading part of the trace anomaly for a free non-relativistic scalar in 2+1 dimensions coupled to a background Newton-Cartan metric. The anomaly is proportional to 1/m, where m is the mass of the scalar. We comment on the implications of a conjectured a-theorem for non-relativistic theories with boost invariance.
Drawing Euler Diagrams with Circles
Stapleton, Gem; Zhang, Leishi; Howse, John; Rodgers, Peter
2010-01-01
Euler diagrams are a popular and intuitive visualization tool which are used in a wide variety of application areas, including biological and medical data analysis. As with other data visualization methods, such as graphs, bar charts, or pie charts, the automated generation of an Euler diagram from a suitable data set would be advantageous, removing the burden of manual data analysis and the subsequent task of drawing an appropriate diagram. Various methods have emerged that automatically dra...
Euler and His Contribution Number Theory
Len, Amy; Scott, Paul
2004-01-01
Born in 1707, Leonhard Euler was the son of a Protestant minister from the vicinity of Basel, Switzerland. With the aim of pursuing a career in theology, Euler entered the University of Basel at the age of thirteen, where he was tutored in mathematics by Johann Bernoulli (of the famous Bernoulli family of mathematicians). He developed an interest…
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…
Energy Technology Data Exchange (ETDEWEB)
Shadid, J.N.; Tuminaro, R.S. [Sandia National Labs., Albuquerque, NM (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States). Dept. of Mathematics and Statistics
1997-02-01
The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript the authors focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context they use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier-Stokes equations with heat and mass transport. The discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.
EULER - A Real Virtual Library for Mathematics
Jost, Michael
2004-01-01
The EULER project completed its work in November 2002. It forms the last part of a very successful project in the specialized but global discipline of mathematics. After a successful RTD project had created the technology, a take-up project has effectively exploited it to the point where its future is assured through a not-for-profit consortium. EULER is a European based, world class, real virtual library for mathematics with up-to-date technological solutions, well accepted by users. In particular, EULER provides a world reference and delivery service, transparent to the end user and offering full coverage of the mathematics literature world-wide, including bibliographic data, peer reviews and/or abstracts, indexing, classification and search, transparent access to library services, co-operation with commercial information providers (publishers, bookstores). The EULER services provide a gateway to the electronic catalogues and repositories of participating institutions, while the latter retain complete respo...
Improving Euler computations at low Mach numbers
Koren, B.; Leer, van B.; Deconinck, H.; Koren, B.
1997-01-01
The paper consists of two parts, both dealing with conditioning techniques for lowMach-number Euler-flow computations, in which a multigrid technique is applied. In the first part, for subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of
Improving Euler computations at low Mach numbers
Koren, B.
1996-01-01
This paper consists of two parts, both dealing with conditioning techniques for low-Mach-number Euler-flow computations, in which a multigrid technique is applied. In the first part, for subsonic flows and upwind-discretized linearized 1-D Euler equations, the smoothing behavior of
Analogues of Euler and Poisson Summation Formulae
Indian Academy of Sciences (India)
... f ( n ) have been obtained in a unified manner, where (()) is a periodic complex sequence; () is the divisor function and () is a sufficiently smooth function on [, ]. We also state a generalised Abel's summation formula, generalised Euler's summation formula and Euler's summation formula in several variables.
Nunan, E.
1973-01-01
Presents a brief biography of Sir Isaac Newton, lists contemporary scientists and scientific developments and discusses Newton's optical research and conceptual position concerning the nature of light. (JR)
Variational problems with fractional derivatives: Euler-Lagrange equations
International Nuclear Information System (INIS)
Atanackovic, T M; Konjik, S; Pilipovic, S
2008-01-01
We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these two bounds coincide, we derive a new form of Euler-Lagrange equations. We use approximations for fractional derivatives in the Lagrangian and obtain the Euler-Lagrange equations which approximate the initial Euler-Lagrange equations in a weak sense
Development of Euler's ideas at the Moscow State Regional University
Vysikaylo, P. I.; Belyaev, V. V.
2018-03-01
In honor of the 250th anniversary of Euler's discovery of three libration points in Russia in 1767 in the area of two rotating gravitational attractors in 2017 an International Interdisciplinary Conference “Euler Readings MRSU 2017” was held in Moscow Region State University (MRSU). The Conference demonstrated that the Euler's ideas continue to remain relevant at the present time. This paper summarizes the main achievements on the basis of Leonard Euler's ideas presented at the Conference.
Isaac Newton's scientific method turning data into evidence about gravity and cosmology
Harper, William L.
2014-01-01
Isaac Newton's Scientific Method examines Newton's argument for universal gravity and his application of it to resolve the problem of deciding between geocentric and heliocentric world systems by measuring masses of the sun and planets. William L. Harper suggests that Newton's inferences from phenomena realize an ideal of empirical success that is richer than prediction. Any theory that can achieve this rich sort of empirical success must not only be able to predict the phenomena it purports to explain, but also have those phenomena accurately measure the parameters which explain them. Harper explores the ways in which Newton's method aims to turn theoretical questions into ones which can be answered empirically by measurement from phenomena, and to establish that propositions inferred from phenomena are provisionally accepted as guides to further research. This methodology, guided by its rich ideal of empirical success, supports a conception of scientific progress that does not require construing it as progr...
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.
Sometimes "Newton's Method" Always "Cycles"
Latulippe, Joe; Switkes, Jennifer
2012-01-01
Are there functions for which Newton's method cycles for all non-trivial initial guesses? We construct and solve a differential equation whose solution is a real-valued function that two-cycles under Newton iteration. Higher-order cycles of Newton's method iterates are explored in the complex plane using complex powers of "x." We find a class of…
An experimental test of Newton's law of gravitation for small accelerations
Energy Technology Data Exchange (ETDEWEB)
Schubert, Sven
2011-10-15
The experiment presented in this thesis has been designed to test Newton's law of gravitation in the limit of small accelerations caused by weak gravitational forces. It is located at DESY, Hamburg, and is a modification of an experiment that was carried out in Wuppertal, Germany, until 2002 in order to measure the gravitational constant G. The idea of testing Newton's law in the case of small accelerations emerged from the question whether the flat rotation curves of spiral galaxies can be traced back to Dark Matter or to a law of gravitation that deviates from Newton on cosmic scales like e.g. MOND (Modified Newtonian Dynamics). The core of this experiment is a microwave resonator which is formed by two spherical concave mirrors that are suspended as pendulums. Masses between 1 and 9 kg symmetrically change their distance to the mirrors from far to near positions. Due to the increased gravitational force the mirrors are pulled apart and the length of the resonator increases. This causes a shift of the resonance frequency which can be translated into a shift of the mirror distance. The small masses are sources of weak gravitational forces and cause accelerations on the mirrors of about 10{sup -10} m/s{sup 2}. These forces are comparable to those between stars on cosmic scales and the accelerations are in the vicinity of the characteristic acceleration of MOND a{sub 0} {approx} 1.2.10{sup -10} m/s{sup 2}, where deviations from Newton's law are expected. Thus Newton's law could be directly checked for correctness under these conditions. First measurements show that due to the sensitivity of this experiment many systematic influences have to be accounted for in order to get consistent results. Newton's law has been confirmed with an accuracy of 3%. MOND has also been checked. In order to be able to distinguish Newton from MOND with other interpolation functions the accuracy of the experiment has to be improved. (orig.)
Combinatorial Aspects of the Generalized Euler's Totient
Directory of Open Access Journals (Sweden)
Nittiya Pabhapote
2010-01-01
Full Text Available A generalized Euler's totient is defined as a Dirichlet convolution of a power function and a product of the Souriau-Hsu-Möbius function with a completely multiplicative function. Two combinatorial aspects of the generalized Euler's totient, namely, its connections to other totients and its relations with counting formulae, are investigated.
Kordy, M. A.; Wannamaker, P. E.; Maris, V.; Cherkaev, E.; Hill, G. J.
2014-12-01
We have developed an algorithm for 3D simulation and inversion of magnetotelluric (MT) responses using deformable hexahedral finite elements that permits incorporation of topography. Direct solvers parallelized on symmetric multiprocessor (SMP), single-chassis workstations with large RAM are used for the forward solution, parameter jacobians, and model update. The forward simulator, jacobians calculations, as well as synthetic and real data inversion are presented. We use first-order edge elements to represent the secondary electric field (E), yielding accuracy O(h) for E and its curl (magnetic field). For very low frequency or small material admittivity, the E-field requires divergence correction. Using Hodge decomposition, correction may be applied after the forward solution is calculated. It allows accurate E-field solutions in dielectric air. The system matrix factorization is computed using the MUMPS library, which shows moderately good scalability through 12 processor cores but limited gains beyond that. The factored matrix is used to calculate the forward response as well as the jacobians of field and MT responses using the reciprocity theorem. Comparison with other codes demonstrates accuracy of our forward calculations. We consider a popular conductive/resistive double brick structure and several topographic models. In particular, the ability of finite elements to represent smooth topographic slopes permits accurate simulation of refraction of electromagnetic waves normal to the slopes at high frequencies. Run time tests indicate that for meshes as large as 150x150x60 elements, MT forward response and jacobians can be calculated in ~2.5 hours per frequency. For inversion, we implemented data space Gauss-Newton method, which offers reduction in memory requirement and a significant speedup of the parameter step versus model space approach. For dense matrix operations we use tiling approach of PLASMA library, which shows very good scalability. In synthetic
New form of the Euler-Bernoulli rod equation applied to robotic systems
Directory of Open Access Journals (Sweden)
Filipović Mirjana
2008-01-01
Full Text Available This paper presents a theoretical background and an example of extending the Euler-Bernoulli equation from several aspects. Euler-Bernoulli equation (based on the known laws of dynamics should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. The stiffness matrix is a full matrix. Damping is an omnipresent elasticity characteristic of real systems, so that it is naturally included in the Euler-Bernoulli equation. It is shown that Daniel Bernoulli's particular integral is just one component of the total elastic deformation of the tip of any mode to which we have to add a component of the elastic deformation of a stationary regime in accordance with the complexity requirements of motion of an elastic robot system. The elastic line equation mode of link of a complex elastic robot system is defined based on the so-called 'Euler-Bernoulli Approach' (EBA. It is shown that the equation of equilibrium of all forces present at mode tip point ('Lumped-mass approach' (LMA follows directly from the elastic line equation for specified boundary conditions. This, in turn, proves the essential relationship between LMA and EBA approaches. In the defined mathematical model of a robotic system with multiple DOF (degree of freedom in the presence of the second mode, the phenomenon of elasticity of both links and joints are considered simultaneously with the presence of the environment dynamics - all based on the previously presented theoretical premises. Simulation results are presented. .
Black Hole Results from XMM-Newton
Directory of Open Access Journals (Sweden)
Norbert Schartel
2014-12-01
Full Text Available XMM-Newton is one of the most successful science missions of the European Space Agency. Since 2003 every year about 300 articles are published in refereed journals making directly use of XMM-Newton data. All XMM-Newton calls for observing proposals are highly oversubscribed by factors of six and more. In the following some scientic highlights of XMM-Newton observations of black holes are summarized.
Isaac Newton: Man, Myth, and Mathematics.
Rickey, V. Frederick
1987-01-01
This article was written in part to celebrate the anniversaries of landmark mathematical works by Newton and Descartes. It's other purpose is to dispel some myths about Sir Isaac Newton and to encourage readers to read Newton's works. (PK)
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)
Conservation of energy for the Euler-Korteweg equations
Dębiec, Tomasz
2017-12-30
In this article we study the principle of energy conservation for the Euler-Korteweg system. We formulate an Onsager-type sufficient regularity condition for weak solutions of the Euler-Korteweg system to conserve the total energy. The result applies to the system of Quantum Hydrodynamics.
Conservation of energy for the Euler-Korteweg equations
Dębiec, Tomasz; Gwiazda, Piotr; Świerczewska-Gwiazda, Agnieszka; Tzavaras, Athanasios
2017-01-01
In this article we study the principle of energy conservation for the Euler-Korteweg system. We formulate an Onsager-type sufficient regularity condition for weak solutions of the Euler-Korteweg system to conserve the total energy. The result applies to the system of Quantum Hydrodynamics.
Newton-Cartan gravity revisited
Andringa, Roel
2016-01-01
In this research Newton's old theory of gravity is rederived using an algebraic approach known as the gauging procedure. The resulting theory is Newton's theory in the mathematical language of Einstein's General Relativity theory, in which gravity is spacetime curvature. The gauging procedure sheds
May, Andrew
2015-01-01
Isaac Newton had an extraordinary idea. He believed the physical universe and everything in it could be described in exact detail using mathematical relationships. He formulated a law of gravity that explained why objects fall downwards, how the moon causes the tides, and why planets and comets orbit the sun. While Newton's work has been added to over the years, his basic approach remains at the heart of the scientific worldview. Yet Newton's own had little in common with that of a modern scientist. He believed the universe was created to a precise and rational design - a design that was fully
Euler European Libraries and Electronic Resources in Mathematical Sciences
The Euler Project. Karlsruhe
The European Libraries and Electronic Resources (EULER) Project in Mathematical Sciences provides the EulerService site for searching out "mathematical resources such as books, pre-prints, web-pages, abstracts, proceedings, serials, technical reports preprints) and NetLab (for Internet resources), this outstanding engine is capable of simple, full, and refined searches. It also offers a browse option, which responds to entries in the author, keyword, and title fields. Further information about the Project is provided at the EULER homepage.
Euler deconvolution and spectral analysis of regional aeromagnetic ...
African Journals Online (AJOL)
Existing regional aeromagnetic data from the south-central Zimbabwe craton has been analysed using 3D Euler deconvolution and spectral analysis to obtain quantitative information on the geological units and structures for depth constraints on the geotectonic interpretation of the region. The Euler solution maps confirm ...
Some Peculiarities of Newton-Hooke Space-Times
Tian, Yu
2011-01-01
Newton-Hooke space-times are the non-relativistic limit of (anti-)de Sitter space-times. We investigate some peculiar facts about the Newton-Hooke space-times, among which the "extraordinary Newton-Hooke quantum mechanics" and the "anomalous Newton-Hooke space-times" are discussed in detail. Analysis on the Lagrangian/action formalism is performed in the discussion of the Newton-Hooke quantum mechanics, where the path integral point of view plays an important role, and the physically measurab...
Energy Technology Data Exchange (ETDEWEB)
Egorov, Yurii V [Institute de Mathematique de Toulouse, Toulouse (France)
2013-04-30
We consider the classical problem on the tallest column which was posed by Euler in 1757. Bernoulli-Euler theory serves today as the basis for the design of high buildings. This problem is reduced to the problem of finding the potential for the Sturm-Liouville equation corresponding to the maximum of the first eigenvalue. The problem has been studied by many mathematicians but we give the first rigorous proof of the existence and uniqueness of the optimal column and we give new formulae which let us find it. Our method is based on a new approach consisting in the study of critical points of a related nonlinear functional. Bibliography: 6 titles.
Leonhard Euler and the mechanics of rigid bodies
Marquina, J. E.; Marquina, M. L.; Marquina, V.; Hernández-Gómez, J. J.
2017-01-01
In this work we present the original ideas and the construction of the rigid bodies theory realised by Leonhard Euler between 1738 and 1775. The number of treatises written by Euler on this subject is enormous, including the most notorious Scientia Navalis (1749), Decouverte d’un noveau principe de mecanique (1752), Du mouvement de rotation des corps solides autour d’un axe variable (1765), Theoria motus corporum solidorum seu rigidorum (1765) and Nova methodus motu corporum rigidorum determinandi (1776), in which he developed the ideas of the instantaneous rotation axis, the so-called Euler equations and angles, the components of what is now known as the inertia tensor, the principal axes of inertia, and, finally, the generalisation of the translation and rotation movement equations for any system. Euler, the man who ‘put most of mechanics into its modern form’ (Truesdell 1968 Essays in the History of Mechanics (Berlin: Springer) p 106).
HIGH-RESOLUTION XMM-NEWTON SPECTROSCOPY OF THE COOLING FLOW CLUSTER A3112
Energy Technology Data Exchange (ETDEWEB)
Bulbul, G. Esra; Smith, Randall K.; Foster, Adam [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Cottam, Jean; Loewenstein, Michael; Mushotzky, Richard; Shafer, Richard, E-mail: ebulbul@cfa.harvard.edu [NASA Goddard Space Flight Center, Greenbelt, MD (United States)
2012-03-01
We examine high signal-to-noise XMM-Newton European Photon Imaging Camera (EPIC) and Reflection Grating Spectrometer (RGS) observations to determine the physical characteristics of the gas in the cool core and outskirts of the nearby rich cluster A3112. The XMM-Newton Extended Source Analysis Software data reduction and background modeling methods were used to analyze the XMM-Newton EPIC data. From the EPIC data, we find that the iron and silicon abundance gradients show significant increase toward the center of the cluster while the oxygen abundance profile is centrally peaked but has a shallower distribution than that of iron. The X-ray mass modeling is based on the temperature and deprojected density distributions of the intracluster medium determined from EPIC observations. The total mass of A3112 obeys the M-T scaling relations found using XMM-Newton and Chandra observations of massive clusters at r{sub 500}. The gas mass fraction f{sub gas} = 0.149{sup +0.036}{sub -0.032} at r{sub 500} is consistent with the seven-year Wilkinson Microwave Anisotropy Probe results. The comparisons of line fluxes and flux limits on the Fe XVII and Fe XVIII lines obtained from high-resolution RGS spectra indicate that there is no spectral evidence for cooler gas associated with the cluster with temperature below 1.0 keV in the central <38'' ({approx}52 kpc) region of A3112. High-resolution RGS spectra also yield an upper limit to the turbulent motions in the compact core of A3112 (206 km s{sup -1}). We find that the contribution of turbulence to total energy is less than 6%. This upper limit is consistent with the energy contribution measured in recent high-resolution simulations of relaxed galaxy clusters.
An inverse method for radiation transport
Energy Technology Data Exchange (ETDEWEB)
Favorite, J. A. (Jeffrey A.); Sanchez, R. (Richard)
2004-01-01
Adjoint functions have been used with forward functions to compute gradients in implicit (iterative) solution methods for inverse problems in optical tomography, geoscience, thermal science, and other fields, but only once has this approach been used for inverse solutions to the Boltzmann transport equation. In this paper, this approach is used to develop an inverse method that requires only angle-independent flux measurements, rather than angle-dependent measurements as was done previously. The method is applied to a simplified form of the transport equation that does not include scattering. The resulting procedure uses measured values of gamma-ray fluxes of discrete, characteristic energies to determine interface locations in a multilayer shield. The method was implemented with a Newton-Raphson optimization algorithm, and it worked very well in numerical one-dimensional spherical test cases. A more sophisticated optimization method would better exploit the potential of the inverse method.
Dr. Euler's fabulous formula Cures many mathematical ills
Nahin, Paul J
2006-01-01
I used to think math was no fun'Cause I couldn't see how it was doneNow Euler's my heroFor I now see why zeroEquals e[pi] i+1--Paul Nahin, electrical engineer In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula--long regarded as the gold standard for mathematical beauty--and shows why it still lies at the heart of complex number theory. This book is the seque
Coupled channels Marchenko inversion for nucleon-nucleon potentials
International Nuclear Information System (INIS)
Kohlhoff, H.; Geramb, H.V. von
1994-01-01
Marchenko inversion is used to determine local energy independent but channel dependent potential matrices from optimum sets of experimental phase shifts. 3 SD 1 and 3 PF 2 channels of nucleon-nucleon systems contain in their off-diagonal potential matrices explicitly the tensor force for T = 0 and 1 isospin. We obtain, together with single channels, complete sets of quantitative nucleon-nucleon potential results which are ready for application in nuclear structure and reaction analyses. The historic coupled channels inversion result of Newton and Fulton is revisited. (orig.)
EVIDENCE FOR AN INTERMEDIATE-MASS BLACK HOLE IN NGC 5408 X-1
International Nuclear Information System (INIS)
Strohmayer, Tod E.; Mushotzky, Richard F.
2009-01-01
We report the discovery with XMM-Newton of correlated spectral and timing behavior in the ultraluminous X-ray source (ULX) NGC 5408 X-1. An ∼100 ks pointing with XMM/Newton obtained in 2008 January reveals a strong 10 mHz quasi-periodic oscillation (QPO) in the >1 keV flux, as well as flat-topped, band-limited noise breaking to a power law. The energy spectrum is again dominated by two components, a 0.16 keV thermal disk and a power law with an index of ∼2.5. These new measurements, combined with results from our previous 2006 January pointing in which we first detected QPOs, show for the first time in a ULX a pattern of spectral and temporal correlations strongly analogous to that seen in Galactic black hole (BH) sources, but at much higher X-ray luminosity and longer characteristic timescales. We find that the QPO frequency is proportional to the inferred disk flux, while the QPO and broadband noise amplitude (rms) are inversely proportional to the disk flux. Assuming that QPO frequency scales inversely with the BH mass at a given power-law spectral index we derive mass estimates using the observed QPO frequency-spectral index relations from five stellar-mass BH systems with dynamical mass constraints. The results from all sources are consistent with a mass range for NGC 5408 X-1 from 1000 to 9000 M sun . We argue that these are conservative limits, and a more likely range is from 2000 to 5000 M sun . Moreover, the recent relation from Gierlinski et al. that relates the BH mass to the strength of variability at high frequencies (above the break in the power spectrum) is also indicative of such a high mass for NGC 5408 X-1. Importantly, none of the above estimates appears consistent with a BH mass less than ∼1000 M sun for NGC 5408 X-1. We argue that these new findings strongly support the conclusion that NGC 5408 X-1 harbors an intermediate-mass BH.
Euler-Poincare reduction for discrete field theories
International Nuclear Information System (INIS)
Vankerschaver, Joris
2007-01-01
In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed
Determination of regional Euler pole parameters for Eastern Austria
Umnig, Elke; Weber, Robert; Schartner, Matthias; Brueckl, Ewald
2017-04-01
The horizontal motion of lithospheric plates can be described as rotations around a rotation axes through the Earth's center. The two possible points where this axes intersects the surface of the Earth are called Euler poles. The rotation is expressed by the Euler parameters in terms of angular velocities together with the latitude and longitude of the Euler pole. Euler parameters were calculated from GPS data for a study area in Eastern Austria. The observation network is located along the Mur-Mürz Valley and the Vienna Basin. This zone is part of the Vienna Transfer Fault, which is the major fault system between the Eastern Alps and the Carpathians. The project ALPAACT (seismological and geodetic monitoring of ALpine-PAnnonian ACtive Tectonics) investigated intra plate tectonic movements within the Austrian part in order to estimate the seismic hazard. Precise site coordinate time series established from processing 5 years of GPS observations are available for the regional network spanning the years from 2010.0 to 2015.0. Station velocities with respect to the global reference frame ITRF2008 have been computed for 23 sites. The common Euler vector was estimated on base of a subset of reliable site velocities, for stations directly located within the area of interest. In a further step a geokinematic interpretation shall be carried out. Therefore site motions with respect to the Eurasian Plate are requested. To obtain this motion field different variants are conceivable. In a simple approach the mean ITRF2008 velocity of IGS site GRAZ can be adopted as Eurasian rotational velocity. An improved alternative is to calculate site-specific velocity differences between the Euler rotation and the individual site velocities. In this poster presentation the Euler parameters, the residual motion field as well as first geokinematic interpretation results are presented.
Truncated Newton-Raphson Methods for Quasicontinuum Simulations
National Research Council Canada - National Science Library
Liang, Yu; Kanapady, Ramdev; Chung, Peter W
2006-01-01
.... In this research, we report the effectiveness of the truncated Newton-Raphson method and quasi-Newton method with low-rank Hessian update strategy that are evaluated against the full Newton-Raphson...
Directory of Open Access Journals (Sweden)
Koh Kim Jie
2017-01-01
Full Text Available Quadratic damping nonlinearity is challenging for displacement based structural dynamics problem as the problem is nonlinear in time derivative of the primitive variable. For such nonlinearity, the formulation of tangent stiffness matrix is not lucid in the literature. Consequently, ambiguity related to kinematics update arises when implementing the time integration-iterative algorithm. In present work, an Euler-Bernoulli beam vibration problem with quadratic damping nonlinearity is addressed as the main source of quadratic damping nonlinearity arises from drag force estimation, which is generally valid only for slender structures. Employing Newton-Raphson formulation, tangent stiffness components associated with quadratic damping nonlinearity requires velocity input for evaluation purpose. For this reason, two mathematically equivalent algorithm structures with different kinematics arrangement are tested. Both algorithm structures result in the same accuracy and convergence characteristic of solution.
A systematic approach to robust preconditioning for gradient-based inverse scattering algorithms
International Nuclear Information System (INIS)
Nordebo, Sven; Fhager, Andreas; Persson, Mikael; Gustafsson, Mats
2008-01-01
This paper presents a systematic approach to robust preconditioning for gradient-based nonlinear inverse scattering algorithms. In particular, one- and two-dimensional inverse problems are considered where the permittivity and conductivity profiles are unknown and the input data consist of the scattered field over a certain bandwidth. A time-domain least-squares formulation is employed and the inversion algorithm is based on a conjugate gradient or quasi-Newton algorithm together with an FDTD-electromagnetic solver. A Fisher information analysis is used to estimate the Hessian of the error functional. A robust preconditioner is then obtained by incorporating a parameter scaling such that the scaled Fisher information has a unit diagonal. By improving the conditioning of the Hessian, the convergence rate of the conjugate gradient or quasi-Newton methods are improved. The preconditioner is robust in the sense that the scaling, i.e. the diagonal Fisher information, is virtually invariant to the numerical resolution and the discretization model that is employed. Numerical examples of image reconstruction are included to illustrate the efficiency of the proposed technique
Turning around Newton's Second Law
Goff, John Eric
2004-01-01
Conceptual and quantitative difficulties surrounding Newton's second law often arise among introductory physics students. Simply turning around how one expresses Newton's second law may assist students in their understanding of a deceptively simple-looking equation.
Stability properties of the Euler-Korteweg system with nonmonotone pressures
Giesselmann, Jan
2016-12-21
We establish a relative energy framework for the Euler-Korteweg system with non-convex energy. This allows us to prove weak-strong uniqueness and to show convergence to a Cahn-Hilliard system in the large friction limit. We also use relative energy to show that solutions of Euler-Korteweg with convex energy converge to solutions of the Euler system in the vanishing capillarity limit, as long as the latter admits sufficiently regular strong solutions.
NITSOL: A Newton iterative solver for nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States)
1996-12-31
Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which the linear systems that characterize Newton steps are solved approximately using iterative linear algebra methods. Here, we outline a well-developed Newton iterative algorithm together with a Fortran implementation called NITSOL. The basic algorithm is an inexact Newton method globalized by backtracking, in which each initial trial step is determined by applying an iterative linear solver until an inexact Newton criterion is satisfied. In the implementation, the user can specify inexact Newton criteria in several ways and select an iterative linear solver from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov solver can be either evaluated analytically with a user-supplied routine or approximated using finite differences of function values. A flexible interface permits a wide variety of preconditioning strategies and allows the user to define a preconditioner and optionally update it periodically. We give details of these and other features and demonstrate the performance of the implementation on a representative set of test problems.
From Moon-fall to motions under inverse square laws
International Nuclear Information System (INIS)
Foong, S K
2008-01-01
The motion of two bodies, along a straight line, under the inverse square law of gravity is considered in detail, progressing from simpler cases to more complex ones: (a) one body fixed and one free, (b) both bodies free and identical mass, (c) both bodies free and different masses and (d) the inclusion of electrostatic forces for both bodies free and different masses. The equations of motion (EOM) are derived starting from Newton's second law or from conservation of energy. They are then reduced to dimensionless EOM using appropriate scales for time and distance. Solutions of the dimensionless EOM as well as the original EOM are given. The time interval for the bodies to fall is expressed as a function of the distance fallen. Formulae for the inverse were obtained. The coalescence times for the different cases are (a) π/2√2 √(L 3 /(Gm 1 )) where L is the initial separation of the two bodies and m 1 is the mass of the fixed body, (b) and (c) t=π/2√2 √(L 3 /(Gm T )) where m T is the total mass of the two bodies and (d) t=π/2√2 √(L 3 /[Gm T (1-Λ)]) where Λ=(kq 1 q 2 )/(Gm 1 m 2 ) and is a measure of the ratio of the electrostatic force to gravity. The last formula may also be used when Λ≥1 with the interpretation that there is no collision if t is infinity or imaginary. We also discuss this motion along the straight line as a special case of the general elliptic motion of two bodies. I believe that this paper will be useful to university tutors as well as undergraduate and even graduate students who prefer to consider the special case before the general case, and their relationship
Huang, Chao-Guang; Guo, Han-Ying; Tian, Yu; Xu, Zhan; Zhou, Bin
2004-01-01
Based on the Beltrami-de Sitter spacetime, we present the Newton-Hooke model under the Newton-Hooke contraction of the $BdS$ spacetime with respect to the transformation group, algebra and geometry. It is shown that in Newton-Hooke space-time, there are inertial-type coordinate systems and inertial-type observers, which move along straight lines with uniform velocity. And they are invariant under the Newton-Hooke group. In order to determine uniquely the Newton-Hooke limit, we propose the Gal...
Leonhard Euler's Wave Theory of Light
DEFF Research Database (Denmark)
Pedersen, Kurt Møller
2008-01-01
is wrong. Most of his mathematical arguments were, however, guesswork without any solid physical reasoning. Guesswork is not always a bad thing in physics if it leads to new experiments or makes the theory coherent with other theories. And Euler tried to find such experiments. He saw the construction......Euler's wave theory of light developed from a mere description of this notion based on an analogy between sound and light to a more and more mathematical elaboration on that notion. He was very successful in predicting the shape of achromatic lenses based on a new dispersion law that we now know...
Drawing Euler Diagrams with Circles: The Theory of Piercings.
Stapleton, Gem; Leishi Zhang; Howse, John; Rodgers, Peter
2011-07-01
Euler diagrams are effective tools for visualizing set intersections. They have a large number of application areas ranging from statistical data analysis to software engineering. However, the automated generation of Euler diagrams has never been easy: given an abstract description of a required Euler diagram, it is computationally expensive to generate the diagram. Moreover, the generated diagrams represent sets by polygons, sometimes with quite irregular shapes that make the diagrams less comprehensible. In this paper, we address these two issues by developing the theory of piercings, where we define single piercing curves and double piercing curves. We prove that if a diagram can be built inductively by successively adding piercing curves under certain constraints, then it can be drawn with circles, which are more esthetically pleasing than arbitrary polygons. The theory of piercings is developed at the abstract level. In addition, we present a Java implementation that, given an inductively pierced abstract description, generates an Euler diagram consisting only of circles within polynomial time.
Identification of the Thermophysical Properties of the Soil by Inverse Problem
Mansour , Salwa; Canot , Édouard; Muhieddine , Mohamad
2016-01-01
International audience; This paper introduces a numerical strategy to estimate the thermophysical properties of a saturated porous medium (volumetric heat capacity (ρC)s , thermal conductivity λs and porosity φ) where a phase change problem (liquid/vapor) appears due strong heating. The estimation of these properties is done by inverse problem knowing the heating curves at selected points of the medium. To solve the inverse problem, we use both the Damped Gauss Newton and the Levenberg Marqua...
Energy Technology Data Exchange (ETDEWEB)
Liu, Yun [Faculty of Information and Automation, Kunming University of Science and Technology, Kunming, Yunnan Province 65005 (China); Zhang, Yin [State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190 (China)
2016-06-08
The mass sensing superiority of a micro/nanomechanical resonator sensor over conventional mass spectrometry has been, or at least, is being firmly established. Because the sensing mechanism of a mechanical resonator sensor is the shifts of resonant frequencies, how to link the shifts of resonant frequencies with the material properties of an analyte formulates an inverse problem. Besides the analyte/adsorbate mass, many other factors such as position and axial force can also cause the shifts of resonant frequencies. The in-situ measurement of the adsorbate position and axial force is extremely difficult if not impossible, especially when an adsorbate is as small as a molecule or an atom. Extra instruments are also required. In this study, an inverse problem of using three resonant frequencies to determine the mass, position and axial force is formulated and solved. The accuracy of the inverse problem solving method is demonstrated and how the method can be used in the real application of a nanomechanical resonator is also discussed. Solving the inverse problem is helpful to the development and application of mechanical resonator sensor on two things: reducing extra experimental equipments and achieving better mass sensing by considering more factors.
Absolute mass scale calibration in the inverse problem of the physical theory of fireballs.
Kalenichenko, V. V.
A method of the absolute mass scale calibration is suggested for solving the inverse problem of the physical theory of fireballs. The method is based on the data on the masses of the fallen meteorites whose fireballs have been photographed in their flight. The method may be applied to those fireballs whose bodies have not experienced considerable fragmentation during their destruction in the atmosphere and have kept their form well enough. Statistical analysis of the inverse problem solution for a sufficiently representative sample makes it possible to separate a subsample of such fireballs. The data on the Lost City and Innisfree meteorites are used to obtain calibration coefficients.
Euler Calculations at Off-Design Conditions for an Inlet of Inward Turning RBCC-SSTO Vehicle
Takashima, N.; Kothari, A. P.
1998-01-01
The inviscid performance of an inward turning inlet design is calculated computationally for the first time. Hypersonic vehicle designs based on the inward turning inlets have been shown analytically to have increased effective specific impulse and lower heat load than comparably designed vehicles with two-dimensional inlets. The inward turning inlets are designed inversely from inviscid stream surfaces of known flow fields. The computational study is performed on a Mach 12 inlet design to validate the performance predicted by the design code (HAVDAC) and calculate its off-design Mach number performance. The three-dimensional Euler equations are solved for Mach 4, 8, and 12 using a software package called SAM, which consists of an unstructured mesh generator (SAMmesh), a three-dimensional unstructured mesh flow solver (SAMcfd), and a CAD-based software (SAMcad). The computed momentum averaged inlet throat pressure is within 6% of the design inlet throat pressure. The mass-flux at the inlet throat is also within 7 % of the value predicted by the design code thereby validating the accuracy of the design code. The off-design Mach number results show that flow spillage is minimal, and the variation in the mass capture ratio with Mach number is comparable to an ideal 2-D inlet. The results from the inviscid flow calculations of a Mach 12 inward turning inlet indicate that the inlet design has very good on and off-design performance which makes it a promising design candidate for future air-breathing hypersonic vehicles.
Euler numbers of four-dimensional rotating black holes with the Euclidean signature
International Nuclear Information System (INIS)
Ma Zhengze
2003-01-01
For a black hole's spacetime manifold in the Euclidean signature, its metric is positive definite and therefore a Riemannian manifold. It can be regarded as a gravitational instanton and a topological characteristic which is the Euler number to which it is associated. In this paper we derive a formula for the Euler numbers of four-dimensional rotating black holes by the integral of the Euler density on the spacetime manifolds of black holes. Using this formula, we obtain that the Euler numbers of Kerr and Kerr-Newman black holes are 2. We also obtain that the Euler number of the Kerr-Sen metric in the heterotic string theory with one boost angle nonzero is 2, which is in accordance with its topology
2012-09-03
27] introduced a new smoothness indicator, which removed the slight post- shock oscillations and improved the convergence . A Newton- iteration method... Gauss - Seidel algorithm for steady Euler equation on unstructured grids, Numer. Math. Theor. Meth. Appl., Vol. 1, pp. 92–112, (2008). [14] G.-S. Jiang...was adopted to solve the steady two dimensional Euler equations [10, 11, 13]. The matrix-free Squared Preconditioning is applied to a Newton iteration
Euler polynomials and identities for non-commutative operators
De Angelis, Valerio; Vignat, Christophe
2015-12-01
Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt [Phys. Rev. D 54(12), 7710-7723 (1996)], expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, by Pain [J. Phys. A: Math. Theor. 46, 035304 (2013)], links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Figuieira de Morisson and Fring [J. Phys. A: Math. Gen. 39, 9269 (2006)] in the context of non-Hermitian Hamiltonian systems. In each case, we provide several proofs and extensions of these identities that highlight the role of Euler and Bernoulli polynomials.
Newton flows for elliptic functions
Helminck, G.F.; Twilt, F.
2015-01-01
Newton flows are dynamical systems generated by a continuous, desingularized Newton method for mappings from a Euclidean space to itself. We focus on the special case of meromorphic functions on the complex plane. Inspired by the analogy between the rational (complex) and the elliptic (i.e., doubly
Introducing Newton and classical physics
Rankin, William
2002-01-01
The rainbow, the moon, a spinning top, a comet, the ebb and flood of the oceans ...a falling apple. There is only one universe and it fell to Isaac Newton to discover its secrets. Newton was arguably the greatest scientific genius of all time, and yet he remains a mysterious figure. Written and illustrated by William Rankin, "Introducting Newton and Classical Physics" explains the extraordinary ideas of a man who sifted through the accumulated knowledge of centuries, tossed out mistaken beliefs, and single-handedly made enormous advances in mathematics, mechanics and optics. By the age of 25, entirely self-taught, he had sketched out a system of the world. Einstein's theories are unthinkable without Newton's founding system. He was also a secret heretic, a mystic and an alchemist, the man of whom Edmund Halley said "Nearer to the gods may no man approach!". This is an ideal companion volume to "Introducing Einstein".
Hall, Alfred Rupert
1982-01-01
The near century (1630–1720) that separates the important astronomical findings of Galileo Galilei (1564–1642) and the vastly influential mathematical work of Sir Isaac Newton (1642–1727) represents a pivotal stage of transition in the history of science. Tracing the revolution in physics initiated by Galileo and culminating in Newton's achievements, this book surveys the work of Huygens, Leeuwenhoek, Boyle, Descartes, and others. 35 illustrations.
Additivity for parametrized topological Euler characteristic and Reidemeister torsion
Badzioch, Bernard; Dorabiala, Wojciech
2005-01-01
Dwyer, Weiss, and Williams have recently defined the notions of parametrized topological Euler characteristic and parametrized topological Reidemeister torsion which are invariants of bundles of compact topological manifolds. We show that these invariants satisfy additivity formulas paralleling the additive properties of the classical Euler characteristic and Reidemeister torsion of finite CW-complexes.
Inverse mass matrix via the method of localized lagrange multipliers
Czech Academy of Sciences Publication Activity Database
González, José A.; Kolman, Radek; Cho, S.S.; Felippa, C.A.; Park, K.C.
2018-01-01
Roč. 113, č. 2 (2018), s. 277-295 ISSN 0029-5981 R&D Projects: GA MŠk(CZ) EF15_003/0000493; GA ČR GA17-22615S Institutional support: RVO:61388998 Keywords : explicit time integration * inverse mass matrix * localized Lagrange multipliers * partitioned analysis Subject RIV: BI - Acoustics OBOR OECD: Applied mechanics Impact factor: 2.162, year: 2016 https://onlinelibrary.wiley.com/doi/10.1002/nme.5613
Subsampled Hessian Newton Methods for Supervised Learning.
Wang, Chien-Chih; Huang, Chun-Heng; Lin, Chih-Jen
2015-08-01
Newton methods can be applied in many supervised learning approaches. However, for large-scale data, the use of the whole Hessian matrix can be time-consuming. Recently, subsampled Newton methods have been proposed to reduce the computational time by using only a subset of data for calculating an approximation of the Hessian matrix. Unfortunately, we find that in some situations, the running speed is worse than the standard Newton method because cheaper but less accurate search directions are used. In this work, we propose some novel techniques to improve the existing subsampled Hessian Newton method. The main idea is to solve a two-dimensional subproblem per iteration to adjust the search direction to better minimize the second-order approximation of the function value. We prove the theoretical convergence of the proposed method. Experiments on logistic regression, linear SVM, maximum entropy, and deep networks indicate that our techniques significantly reduce the running time of the subsampled Hessian Newton method. The resulting algorithm becomes a compelling alternative to the standard Newton method for large-scale data classification.
Milgrom's revision of Newton's laws: Dynamical and cosmological consequences
International Nuclear Information System (INIS)
Felten, J.E.; and University of Maryland, College Park)
1984-01-01
Milgrom's recent revision of Newtonian dynamics was introduced to eliminate the inference that large quantities of invisible mass exist in galaxies. I show by simple examples that a Milgrom acceleration, in the form presented so far, implies other far-reaching changes in dynamics. The momentum of an isolated system is not conserved, and the usual theorem for center-of-mass motion of any system does not hold. Naive applications require extreme caution. The model fails to provide a complete description of particle dynamics and should be thought of as a revision of Kepler's laws rather than Newton's
Euler-Lagrange Equations of Networks with Higher-Order Elements
Directory of Open Access Journals (Sweden)
Z. Biolek
2017-06-01
Full Text Available The paper suggests a generalization of the classic Euler-Lagrange equation for circuits compounded of arbitrary elements from Chua’s periodic table. Newly defined potential functions for general (α, β elements are used for the construction of generalized Lagrangians and generalized dissipative functions. Also procedures of drawing the Euler-Lagrange equations are demonstrated.
Mitochondrial mass is inversely correlated to complete lipid oxidation in human myotubes
DEFF Research Database (Denmark)
Gaster, Michael
2011-01-01
Exercise increases while physical inactivity decrease mitochondrial content and oxidative capacity of skeletal muscles in vivo. It is unknown whether mitochondrial mass and substrate oxidation are related in non-contracting skeletal muscle. Mitochondrial mass, ATP, ADP, AMP, glucose and lipid......, basal glucose oxidation and incomplete lipid oxidation were significantly increased while complete lipid oxidation was lower. Mitochondrial mass was not correlated to glucose oxidation or incomplete lipid oxidation in human myotubes but inversely correlated to complete lipid oxidation. Thus within...... a stable energetic background, an increased mitochondrial mass in human myotubes was not positive correlated to an increased substrate oxidation as expected from skeletal muscles in vivo but surprisingly with a reduced complete lipid oxidation....
Lee, Kiju; Wang, Yunfeng; Chirikjian, Gregory S
2007-11-01
Over the past several decades a number of O(n) methods for forward and inverse dynamics computations have been developed in the multi-body dynamics and robotics literature. A method was developed in 1974 by Fixman for O(n) computation of the mass-matrix determinant for a serial polymer chain consisting of point masses. In other recent papers, we extended this method in order to compute the inverse of the mass matrix for serial chains consisting of point masses. In the present paper, we extend these ideas further and address the case of serial chains composed of rigid-bodies. This requires the use of relatively deep mathematics associated with the rotation group, SO(3), and the special Euclidean group, SE(3), and specifically, it requires that one differentiates functions of Lie-group-valued argument.
Newton's Cradle in Physics Education
Gauld, Colin F.
2006-01-01
Newton's Cradle is a series of bifilar pendulums used in physics classrooms to demonstrate the role of the principles of conservation of momentum and kinetic energy in elastic collisions. The paper reviews the way in which textbooks use Newton's Cradle and points out the unsatisfactory nature of these treatments in almost all cases. The literature…
An experiment for determining the Euler load by direct computation
Thurston, Gaylen A.; Stein, Peter A.
1986-01-01
A direct algorithm is presented for computing the Euler load of a column from experimental data. The method is based on exact inextensional theory for imperfect columns, which predicts two distinct deflected shapes at loads near the Euler load. The bending stiffness of the column appears in the expression for the Euler load along with the column length, therefore the experimental data allows a direct computation of bending stiffness. Experiments on graphite-epoxy columns of rectangular cross-section are reported in the paper. The bending stiffness of each composite column computed from experiment is compared with predictions from laminated plate theory.
Newton's Metaphysics of Space as God's Emanative Effect
Jacquette, Dale
2014-09-01
In several of his writings, Isaac Newton proposed that physical space is God's "emanative effect" or "sensorium," revealing something interesting about the metaphysics underlying his mathematical physics. Newton's conjectures depart from Plato and Aristotle's metaphysics of space and from classical and Cambridge Neoplatonism. Present-day philosophical concepts of supervenience clarify Newton's ideas about space and offer a portrait of Newton not only as a mathematical physicist but an independent-minded rationalist philosopher.
Euler Polynomials and Identities for Non-Commutative Operators
De Angelis, V.; Vignat, C.
2015-01-01
Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt, expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, due to J.-C. Pain, links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Fig...
Energy Technology Data Exchange (ETDEWEB)
Deshpande, Amruta J.; Hughes, John P. [Department of Physics and Astronomy, Rutgers the State University of New Jersey, 136 Frelinghuysen Road, Piscataway, NJ 08854 (United States); Wittman, David, E-mail: amrejd@physics.rutgers.edu, E-mail: jph@physics.rutgers.edu, E-mail: dwittman@physics.ucdavis.edu [Department of Physics, University of California, Davis, One Shields Avenue, Davis, CA 95616 (United States)
2017-04-20
We continue the study of the first sample of shear-selected clusters from the initial 8.6 square degrees of the Deep Lens Survey (DLS); a sample with well-defined selection criteria corresponding to the highest ranked shear peaks in the survey area. We aim to characterize the weak lensing selection by examining the sample’s X-ray properties. There are multiple X-ray clusters associated with nearly all the shear peaks: 14 X-ray clusters corresponding to seven DLS shear peaks. An additional three X-ray clusters cannot be definitively associated with shear peaks, mainly due to large positional offsets between the X-ray centroid and the shear peak. Here we report on the XMM-Newton properties of the 17 X-ray clusters. The X-ray clusters display a wide range of luminosities and temperatures; the L {sub X} − T {sub X} relation we determine for the shear-associated X-ray clusters is consistent with X-ray cluster samples selected without regard to dynamical state, while it is inconsistent with self-similarity. For a subset of the sample, we measure X-ray masses using temperature as a proxy, and compare to weak lensing masses determined by the DLS team. The resulting mass comparison is consistent with equality. The X-ray and weak lensing masses show considerable intrinsic scatter (∼48%), which is consistent with X-ray selected samples when their X-ray and weak lensing masses are independently determined.
Low-rank Quasi-Newton updates for Robust Jacobian lagging in Newton methods
International Nuclear Information System (INIS)
Brown, J.; Brune, P.
2013-01-01
Newton-Krylov methods are standard tools for solving nonlinear problems. A common approach is to 'lag' the Jacobian when assembly or preconditioner setup is computationally expensive, in exchange for some degradation in the convergence rate and robustness. We show that this degradation may be partially mitigated by using the lagged Jacobian as an initial operator in a quasi-Newton method, which applies unassembled low-rank updates to the Jacobian until the next full reassembly. We demonstrate the effectiveness of this technique on problems in glaciology and elasticity. (authors)
Newton flows for elliptic functions: A pilot study
Twilt, F.; Helminck, G.F.; Snuverink, M.; van den Brug, L.
2008-01-01
Elliptic Newton flows are generated by a continuous, desingularized Newton method for doubly periodic meromorphic functions on the complex plane. In the special case, where the functions underlying these elliptic Newton flows are of second-order, we introduce various, closely related, concepts of
Dark Matter Search Using XMM-Newton Observations of Willman 1
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.
Uncertainty Quantification for Large-Scale Ice Sheet Modeling
Energy Technology Data Exchange (ETDEWEB)
Ghattas, Omar [Univ. of Texas, Austin, TX (United States)
2016-02-05
This report summarizes our work to develop advanced forward and inverse solvers and uncertainty quantification capabilities for a nonlinear 3D full Stokes continental-scale ice sheet flow model. The components include: (1) forward solver: a new state-of-the-art parallel adaptive scalable high-order-accurate mass-conservative Newton-based 3D nonlinear full Stokes ice sheet flow simulator; (2) inverse solver: a new adjoint-based inexact Newton method for solution of deterministic inverse problems governed by the above 3D nonlinear full Stokes ice flow model; and (3) uncertainty quantification: a novel Hessian-based Bayesian method for quantifying uncertainties in the inverse ice sheet flow solution and propagating them forward into predictions of quantities of interest such as ice mass flux to the ocean.
The Camassa-Holm equation as an incompressible Euler equation: A geometric point of view
Gallouët, Thomas; Vialard, François-Xavier
2018-04-01
The group of diffeomorphisms of a compact manifold endowed with the L2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently, several authors have extended optimal transport to the space of positive Radon measures where the Wasserstein-Fisher-Rao distance is a natural extension of the classical L2-Wasserstein distance. In this paper, we show a similar relation between this unbalanced optimal transport problem and the Hdiv right-invariant metric on the group of diffeomorphisms, which corresponds to the Camassa-Holm (CH) equation in one dimension. Geometrically, we present an isometric embedding of the group of diffeomorphisms endowed with this right-invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an L2 type of cone metric. This leads to a new formulation of the (generalized) CH equation as a geodesic equation on an isotropy subgroup of this automorphisms group; On S1, solutions to the standard CH thus give radially 1-homogeneous solutions of the incompressible Euler equation on R2 which preserves a radial density that has a singularity at 0. An other application consists in proving that smooth solutions of the Euler-Arnold equation for the Hdiv right-invariant metric are length minimizing geodesics for sufficiently short times.
Petit, Jean-Pierre; D'Agostini, G.
2015-03-01
We reconsider the classical Schwarzschild solution in the context of a Janus cosmological model. We show that the central singularity can be eliminated through a simple coordinate change and that the subsequent transit from one fold to the other is accompanied by mass inversion. In such scenario matter swallowed by black holes could be ejected as invisible negative mass and dispersed in space.
DEFF Research Database (Denmark)
Strykowski, Gabriel; Larsen, Jacob Norby
2000-01-01
In this paper we advocate the use of Newton's law of gravitational attraction to ensure perfect consistency between gravity and height data. Starting with the absolute gravity on the topography we decompose this signal into a number of quantities associated with physics of the system. To model...... gravitational attraction from topography we use DTM and Newton's law of gravitational attraction. A residual part of the gravity signal is interpreted as inconsistency between gravity and heights. In the paper we discuss a method by which such inconsistency (at least in principle) can be decomposed...
Euler's pioneering equation the most beautiful theorem in mathematics
Wilson, Robin
2018-01-01
In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence."
Efficient Inversion of Mult-frequency and Multi-Source Electromagnetic Data
Energy Technology Data Exchange (ETDEWEB)
Gary D. Egbert
2007-03-22
The project covered by this report focused on development of efficient but robust non-linear inversion algorithms for electromagnetic induction data, in particular for data collected with multiple receivers, and multiple transmitters, a situation extremely common in eophysical EM subsurface imaging methods. A key observation is that for such multi-transmitter problems each step in commonly used linearized iterative limited memory search schemes such as conjugate gradients (CG) requires solution of forward and adjoint EM problems for each of the N frequencies or sources, essentially generating data sensitivities for an N dimensional data-subspace. These multiple sensitivities allow a good approximation to the full Jacobian of the data mapping to be built up in many fewer search steps than would be required by application of textbook optimization methods, which take no account of the multiplicity of forward problems that must be solved for each search step. We have applied this idea to a develop a hybrid inversion scheme that combines features of the iterative limited memory type methods with a Newton-type approach using a partial calculation of the Jacobian. Initial tests on 2D problems show that the new approach produces results essentially identical to a Newton type Occam minimum structure inversion, while running more rapidly than an iterative (fixed regularization parameter) CG style inversion. Memory requirements, while greater than for something like CG, are modest enough that even in 3D the scheme should allow 3D inverse problems to be solved on a common desktop PC, at least for modest (~ 100 sites, 15-20 frequencies) data sets. A secondary focus of the research has been development of a modular system for EM inversion, using an object oriented approach. This system has proven useful for more rapid prototyping of inversion algorithms, in particular allowing initial development and testing to be conducted with two-dimensional example problems, before
Newtonian cosmology Newton would understand
International Nuclear Information System (INIS)
Lemons, D.S.
1988-01-01
Isaac Newton envisioned a static, infinite, and initially uniform, zero field universe that was gravitationally unstable to local condensations of matter. By postulating the existence of such a universe and using it as a boundary condition on Newtonian gravity, a new field equation for gravity is derived, which differs from the classical one by a time-dependent cosmological term proportional to the average mass density of the universe. The new field equation not only makes Jeans' analysis of the gravitational instability of a Newtonian universe consistent, but also gives rise to a family of Newtonian evolutionary cosmologies parametrized by a time-invariant expansion velocity. This Newtonian cosmology contrasts with both 19th-century ones and with post general relativity Newtonian cosmology
Swimming holonomy principles, exemplified with a Euler fluid in two dimensions
International Nuclear Information System (INIS)
Hannay, J H
2012-01-01
principle, a completely solvable case is analyzed: that of a Euler fluid where the swimmer's shape is fixed but its internal mass distribution varies cyclically. (paper)
Indian Academy of Sciences (India)
It is not hard to show that the series converges, for by com- bining pairs of terms it can be ..... not escape Euler's attention-but then few things did!) We consider the function ... the proof. In particular there is no such thing as an unrig- orous proof.
Short-range inverse-square law experiment in space
International Nuclear Information System (INIS)
Strayer, D.M.; Paik, H.J.; Moody, M.V.
2003-01-01
The objective of ISLES (inverse-square law experiment in space) is to perform a null test of Newton's law on the ISS with a resolution of one part in 10 5 at ranges from 100 mm to 1 mm. ISLES will be sensitive enough to detect axions with the strongest allowed coupling and to test the string-theory prediction with R>= 5 μm. To accomplish these goals on the rather noisy International Space Station, the experiment is set up to provide immunity from the vibrations and other common-mode accelerations. The measures to be applied for reducing the effects of disturbances will be described in this presentation. As designed, the experiment will be cooled to less than 2 K in NASA's low temperature facility the LTMPF, allowing superconducting magnetic levitation in microgravity to obtain very soft, low-loss suspension of the test masses. The low-damping magnetic levitation, combined with a low-noise SQUID, leads to extremely low intrinsic noise in the detector. To minimize Newtonian errors, ISLES employs a near-null source of gravity, a circular disk of large diameter-to-thickness ratio. Two test masses, also disk-shaped, are suspended on the two sides of the source mass at a distance of 100 μm to 1 mm. The signal is detected by a superconducting differential accelerometer, making a highly sensitive sensor of the gravity force generated by the source mass
Euler's fluid equations: Optimal control vs optimization
International Nuclear Information System (INIS)
Holm, Darryl D.
2009-01-01
An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the Eulerian velocity vector field. Thus, an optimal control problem and an optimization problem for incompressible ideal fluid flow both yield the same Euler fluid equations, although their Lagrangian parcel dynamics are different. This is a result of the gauge freedom in the definition of the fluid pressure for an incompressible flow, in combination with the symmetry of fluid dynamics under relabeling of their Lagrangian coordinates. Similar ideas are also illustrated for SO(N) rigid body motion.
Choosing the forcing terms in an inexact Newton method
Energy Technology Data Exchange (ETDEWEB)
Eisenstat, S.C. [Yale Univ., New Haven, CT (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States)
1994-12-31
An inexact Newton method is a generalization of Newton`s method for solving F(x) = 0, F: {Re}{sup n} {r_arrow} {Re}{sup n}, in which each step reduces the norm of the local linear model of F. At the kth iteration, the norm reduction is usefully expressed by the inexact Newton condition where x{sub k} is the current approximate solution and s{sub k} is the step. In many applications, an {eta}{sub k} is first specified, and then an S{sub k} is found for which the inexact Newton condition holds. Thus {eta}{sub k} is often called a {open_quotes}forcing term{close_quotes}. In practice, the choice of the forcing terms is usually critical to the efficiency of the method and can affect robustness as well. Here, the authors outline several promising choices, discuss theoretical support for them, and compare their performance in a Newton iterative (truncated Newton) method applied to several large-scale problems.
"To Improve upon Hints of Things": Illustrating Isaac Newton.
Schilt, Cornelis J
2016-01-01
When Isaac Newton died in 1727 he left a rich legacy in terms of draft manuscripts, encompassing a variety of topics: natural philosophy, mathematics, alchemy, theology, and chronology, as well as papers relating to his career at the Mint. One thing that immediately strikes us is the textuality of Newton's legacy: images are sparse. Regarding his scholarly endeavours we witness the same practice. Newton's extensive drafts on theology and chronology do not contain a single illustration or map. Today we have all of Newton's draft manuscripts as witnesses of his working methods, as well as access to a significant number of books from his own library. Drawing parallels between Newton's reading practices and his natural philosophical and scholarly work, this paper seeks to understand Newton's recondite writing and publishing politics.
Photon and graviton mass limits
International Nuclear Information System (INIS)
Goldhaber, Alfred Scharff; Nieto, Michael Martin
2010-01-01
Efforts to place limits on deviations from canonical formulations of electromagnetism and gravity have probed length scales increasing dramatically over time. Historically, these studies have passed through three stages: (1) testing the power in the inverse-square laws of Newton and Coulomb, (2) seeking a nonzero value for the rest mass of photon or graviton, and (3) considering more degrees of freedom, allowing mass while preserving explicit gauge or general-coordinate invariance. Since the previous review the lower limit on the photon Compton wavelength has improved by four orders of magnitude, to about one astronomical unit, and rapid current progress in astronomy makes further advance likely. For gravity there have been vigorous debates about even the concept of graviton rest mass. Meanwhile there are striking observations of astronomical motions that do not fit Einstein gravity with visible sources. ''Cold dark matter'' (slow, invisible classical particles) fits well at large scales. ''Modified Newtonian dynamics'' provides the best phenomenology at galactic scales. Satisfying this phenomenology is a requirement if dark matter, perhaps as invisible classical fields, could be correct here too. ''Dark energy''might be explained by a graviton-mass-like effect, with associated Compton wavelength comparable to the radius of the visible universe. Significant mass limits are summarized in a table.
Photon and graviton mass limits
Goldhaber, Alfred Scharff; Nieto, Michael Martin
2010-01-01
Efforts to place limits on deviations from canonical formulations of electromagnetism and gravity have probed length scales increasing dramatically over time. Historically, these studies have passed through three stages: (1) testing the power in the inverse-square laws of Newton and Coulomb, (2) seeking a nonzero value for the rest mass of photon or graviton, and (3) considering more degrees of freedom, allowing mass while preserving explicit gauge or general-coordinate invariance. Since the previous review the lower limit on the photon Compton wavelength has improved by four orders of magnitude, to about one astronomical unit, and rapid current progress in astronomy makes further advance likely. For gravity there have been vigorous debates about even the concept of graviton rest mass. Meanwhile there are striking observations of astronomical motions that do not fit Einstein gravity with visible sources. “Cold dark matter” (slow, invisible classical particles) fits well at large scales. “Modified Newtonian dynamics” provides the best phenomenology at galactic scales. Satisfying this phenomenology is a requirement if dark matter, perhaps as invisible classical fields, could be correct here too. “Dark energy” might be explained by a graviton-mass-like effect, with associated Compton wavelength comparable to the radius of the visible universe. Significant mass limits are summarized in a table.
ENTROPIES AND FLUX-SPLITTINGS FOR THE ISENTROPIC EULER EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The authors establish the existence of a large class of mathematical entropies (the so-called weak entropies) associated with the Euler equations for an isentropic, compressible fluid governed by a general pressure law. A mild assumption on the behavior of the pressure law near the vacuum is solely required. The analysis is based on an asymptotic expansion of the fundamental solution (called here the entropy kernel) of a highly singular Euler-Poisson-Darboux equation. The entropy kernel is only H lder continuous and its regularity is carefully investigated. Relying on a notion introduced earlier by the authors, it is also proven that, for the Euler equations, the set of entropy flux-splittings coincides with the set of entropies-entropy fluxes. These results imply the existence of a flux-splitting consistent with all of the entropy inequalities.
On the Euler Function of the Catalan Numbers
2012-02-26
ON THE EULER FUNCTION OF THE CATALAN NUMBERS FLORIAN LUCA AND PANTELIMON STĂNICĂ Abstract. We study the solutions of the equation φ(Cm)/φ(Cn) = r...where r is a fixed rational number , Ck is the kth Catalan number and φ is the Euler function. We note that the number r = 4 is special for this...observation concerning φ(Cn+1)/φ(Cn) For a positive integer n, let (1) Cn = 1 n+ 1 ( 2n n ) be the n-th Catalan number . For a positive integer m we put φ(m) for
Beyond Euler's Method: Implicit Finite Differences in an Introductory ODE Course
Kull, Trent C.
2011-01-01
A typical introductory course in ordinary differential equations (ODEs) exposes students to exact solution methods. However, many differential equations must be approximated with numerical methods. Textbooks commonly include explicit methods such as Euler's and Improved Euler's. Implicit methods are typically introduced in more advanced courses…
Newton-Cartan gravity and torsion
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.
Gravity in minesmdashAn investigation of Newton's law
International Nuclear Information System (INIS)
Holding, S.C.; Stacey, F.D.; Tuck, G.J.
1986-01-01
The evidence that the value of the Newtonian gravitational constant G inferred from measurements of gravity g in mines and boreholes is of order 1% higher than the laboratory value is hardened with new and improved data from two mines in northwest Queensland. Surface-gravity surveys and more than 14 000 bore-core density values have been used to establish density structures for the mines, permitting full three-dimensional inversion to obtain G. Further constraint is imposed by requiring that the density structure give the same value of G for several vertical profiles of g, separated by hundreds of meters. The only residual doubt arises from the possibility of bias by an anomalous regional gravity gradient. Neither measurements of gravity gradient above ground level (in tall chimneys) nor surface surveys are yet adequate to remove this doubt, but the coincidence of conclusions derived from mine data obtained in different parts of the world makes such an anomaly appear an improbable explanation. If Newton's law is modified by adding a Yukawa term to the gravitational potential of a point mass m at distance r, V = -(G/sub infinity/m/r)(1+αe/sup -r/lambda/), then the mine data provide a mutual constraint on the values of α and lambda, although they cannot be determined independently. Our results give αroughly-equal-0.0075 if lambda or =10 4 m, with intermediate values of α between these ranges, but values greater than α = -0.010, lambda = 800 m appear to be disallowed by a comparison of satellite and land-surface estimates of gravity
On topological modifications of Newton's law
International Nuclear Information System (INIS)
Floratos, E.G.; Leontaris, G.K.
2012-01-01
Recent cosmological data for very large distances challenge the validity of the standard cosmological model. Motivated by the observed spatial flatness the accelerating expansion and the various anisotropies with preferred axes in the universe we examine the consequences of the simple hypothesis that the three-dimensional space has a global R 2 × S 1 topology. We take the radius of the compactification to be the observed cosmological scale beyond which the accelerated expansion starts. We derive the induced corrections to the Newton's gravitational potential and we find that for distances smaller than the S 1 radius the leading 1/r-term is corrected by convergent power series of multipole form in the polar angle making explicit the induced anisotropy by the compactified third dimension. On the other hand, for distances larger than the compactification scale the asymptotic behavior of the potential exhibits a logarithmic dependence with exponentially small corrections. The change of Newton's force from 1/r 2 to 1/r behavior implies a weakening of the deceleration for the expanding universe. Such topologies can also be created locally by standard Newtonian axially symmetric mass distributions with periodicity along the symmetry axis. In such cases we can use our results to obtain measurable modifications of Newtonian orbits for small distances and flat rotation spectra, for large distances at the galactic level
On Newton-Cartan trace anomalies
International Nuclear Information System (INIS)
Auzzi, Roberto; Baiguera, Stefano; Nardelli, Giuseppe
2016-01-01
We classify the trace anomaly for parity-invariant non-relativistic Schrödinger theories in 2+1 dimensions coupled to background Newton-Cartan gravity. The general anomaly structure looks very different from the one in the z=2 Lifshitz theories. The type A content of the anomaly is remarkably identical to that of the relativistic 3+1 dimensional case, suggesting the conjecture that an a-theorem should exist also in the Newton-Cartan context.
On Newton-Cartan trace anomalies
Energy Technology Data Exchange (ETDEWEB)
Auzzi, Roberto [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); INFN Sezione di Perugia,Via A. Pascoli, 06123 Perugia (Italy); Baiguera, Stefano [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); Nardelli, Giuseppe [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); TIFPA - INFN, c/o Dipartimento di Fisica, Università di Trento,38123 Povo (Italy)
2016-02-01
We classify the trace anomaly for parity-invariant non-relativistic Schrödinger theories in 2+1 dimensions coupled to background Newton-Cartan gravity. The general anomaly structure looks very different from the one in the z=2 Lifshitz theories. The type A content of the anomaly is remarkably identical to that of the relativistic 3+1 dimensional case, suggesting the conjecture that an a-theorem should exist also in the Newton-Cartan context.
Directory of Open Access Journals (Sweden)
Dae San Kim
2012-01-01
Full Text Available We derive some interesting identities and arithmetic properties of Bernoulli and Euler polynomials from the orthogonality of Hermite polynomials. Let Pn={p(x∈ℚ[x]∣deg p(x≤n} be the (n+1-dimensional vector space over ℚ. Then we show that {H0(x,H1(x,…,Hn(x} is a good basis for the space Pn for our purpose of arithmetical and combinatorial applications.
Van der Kallen, Wilberd|info:eu-repo/dai/nl/117156108
2015-01-01
Let R be a noetherian ring of dimension d and let n be an integer so that n≤d≤2n-3. Let (a
Cao, Qing; Nastac, Laurentiu
2018-06-01
In this study, the Euler-Euler and Euler-Lagrange modeling approaches were applied to simulate the multiphase flow in the water model and gas-stirred ladle systems. Detailed comparisons of the computational and experimental results were performed to establish which approach is more accurate for predicting the gas-liquid multiphase flow phenomena. It was demonstrated that the Euler-Lagrange approach is more accurate than the Euler-Euler approach. The Euler-Lagrange approach was applied to study the effects of the free surface setup, injected bubble size, gas flow rate, and slag layer thickness on the slag-steel interaction and mass transfer behavior. Detailed discussions on the flat/non-flat free surface assumption were provided. Significant inaccuracies in the prediction of the surface fluid flow characteristics were found when the flat free surface was assumed. The variations in the main controlling parameters (bubble size, gas flow rate, and slag layer thickness) and their potential impact on the multiphase fluid flow and mass transfer characteristics (turbulent intensity, mass transfer rate, slag-steel interfacial area, flow patterns, etc.,) in gas-stirred ladles were quantitatively determined to ensure the proper increase in the ladle refining efficiency. It was revealed that by injecting finer bubbles as well as by properly increasing the gas flow rate and the slag layer thickness, the ladle refining efficiency can be enhanced significantly.
Goethe's Exposure of Newton's theory a polemic on Newton's theory of light and colour
Goethe, Johann Wolfgang von
2016-01-01
Johann Wolfgang von Goethe, although best known for his literary work, was also a keen and outspoken natural scientist. In the second polemic part of Zur Farbenlehre (Theory of Colours), for example, Goethe attacked Isaac Newton's ground-breaking revelation that light is heterogeneous and not immutable, as was previously thought.This polemic was unanimously rejected by the physicists of the day, and has often been omitted from compendia of Goethe's works. Indeed, although Goethe repeated all of Newton's key experiments, he was never able to achieve the same results. Many reasons have been proposed for this, ranging from the psychological — such as a blind hatred of Newtonism, self-deceit and paranoid psychosis — to accusations of incapability — Goethe simply did not understand the experiments. Yet Goethe was never to be dissuaded from this passionate conviction.This translation of Goethe's second polemic, published for the first time in English, makes it clear that Goethe did understand the thrust of Ne...
3D CSEM inversion based on goal-oriented adaptive finite element method
Zhang, Y.; Key, K.
2016-12-01
We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with
Energy Technology Data Exchange (ETDEWEB)
Mernild, Sebastian Haugard [Los Alamos National Laboratory; Liston, Glen [COLORADO STATE UNIV.
2009-01-01
In many applications, a realistic description of air temperature inversions is essential for accurate snow and glacier ice melt, and glacier mass-balance simulations. A physically based snow-evolution modeling system (SnowModel) was used to simulate eight years (1998/99 to 2005/06) of snow accumulation and snow and glacier ice ablation from numerous small coastal marginal glaciers on the SW-part of Ammassalik Island in SE Greenland. These glaciers are regularly influenced by inversions and sea breezes associated with the adjacent relatively low temperature and frequently ice-choked fjords and ocean. To account for the influence of these inversions on the spatiotemporal variation of air temperature and snow and glacier melt rates, temperature inversion routines were added to MircoMet, the meteorological distribution sub-model used in SnowModel. The inversions were observed and modeled to occur during 84% of the simulation period. Modeled inversions were defined not to occur during days with strong winds and high precipitation rates due to the potential of inversion break-up. Field observations showed inversions to extend from sea level to approximately 300 m a.s.l., and this inversion level was prescribed in the model simulations. Simulations with and without the inversion routines were compared. The inversion model produced air temperature distributions with warmer lower elevation areas and cooler higher elevation areas than without inversion routines due to the use of cold sea-breeze base temperature data from underneath the inversion. This yielded an up to 2 weeks earlier snowmelt in the lower areas and up to 1 to 3 weeks later snowmelt in the higher elevation areas of the simulation domain. Averaged mean annual modeled surface mass-balance for all glaciers (mainly located above the inversion layer) was -720 {+-} 620 mm w.eq. y{sup -1} for inversion simulations, and -880 {+-} 620 mm w.eq. y{sup -1} without the inversion routines, a difference of 160 mm w.eq. y
Field-Split Preconditioned Inexact Newton Algorithms
Liu, Lulu
2015-06-02
The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm is presented as a complement to additive Schwarz preconditioned inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. We consider both types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Numerical experiments show that MSPIN can be significantly more robust than Newton methods based on global linearizations, and that MSPIN can be more robust than ASPIN and maintain fast convergence even for challenging problems, such as high Reynolds number Navier--Stokes equations.
Field-Split Preconditioned Inexact Newton Algorithms
Liu, Lulu; Keyes, David E.
2015-01-01
The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm is presented as a complement to additive Schwarz preconditioned inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. We consider both types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Numerical experiments show that MSPIN can be significantly more robust than Newton methods based on global linearizations, and that MSPIN can be more robust than ASPIN and maintain fast convergence even for challenging problems, such as high Reynolds number Navier--Stokes equations.
Newton-type methods for optimization and variational problems
Izmailov, Alexey F
2014-01-01
This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will b...
Euler-Poincare Reduction of a Rigid Body Motion
DEFF Research Database (Denmark)
Wisniewski, Rafal; Kulczycki, P.
2005-01-01
|If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system afected by an external force of a control action....... Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincare reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modeling, estimation and control of mechanical systems......-known Euler-Poincare reduction to a rigid body motion with forcing....
Newton's law in de Sitter brane
International Nuclear Information System (INIS)
Ghoroku, Kazuo; Nakamura, Akihiro; Yahiro, Masanobu
2003-01-01
Newton potential has been evaluated for the case of dS brane embedded in Minkowski, dS 5 and AdS 5 bulks. We point out that only the AdS 5 bulk might be consistent with the Newton's law from the brane-world viewpoint when we respect a small cosmological constant observed at present universe
3, 2, 1 ... Discovering Newton's Laws
Lutz, Joe; Sylvester, Kevin; Oliver, Keith; Herrington, Deborah
2017-01-01
"For every action there is an equal and opposite reaction." "Except when a bug hits your car window, the car must exert more force on the bug because Newton's laws only apply in the physics classroom, right?" Students in our classrooms were able to pick out definitions as well as examples of Newton's three laws; they could…
Exact, rotational, infinite energy, blowup solutions to the 3-dimensional Euler equations
International Nuclear Information System (INIS)
Yuen, Manwai
2011-01-01
In this Letter, we construct a new class of blowup or global solutions with elementary functions to the 3-dimensional compressible or incompressible Euler and Navier-Stokes equations. And the corresponding blowup or global solutions for the incompressible Euler and Naiver-Stokes equations are also given. Our constructed solutions are similar to the famous Arnold-Beltrami-Childress (ABC) flow. The obtained solutions with infinite energy can exhibit the interesting behaviors locally. Furthermore, due to divu → =0 for the solutions, the solutions also work for the 3-dimensional incompressible Euler and Navier-Stokes equations. -- Highlights: → We construct a new class of solutions to the 3D compressible or incompressible Euler and Navier-Stokes equations. → The constructed solutions are similar to the famous Arnold-Beltrami-Childress flow. → The solutions with infinite energy can exhibit the interesting behaviors locally.
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.
Using an SLR inversion to measure the mass balance of Greenland before and during GRACE
Bonin, Jennifer
2016-04-01
The GRACE mission has done an admirable job of measuring large-scale mass changes over Greenland since its launch in 2002. However before that time, measurements of large-scale ice mass balance were few and far between, leading to a lack of baseline knowledge. High-quality Satellite Laser Ranging (SLR) data existed a decade earlier, but normally has too low a spatial resolution to be used for this purpose. I demonstrate that a least squares inversion technique can reconstitute the SLR data and use it to measure ice loss over Greenland. To do so, I first simulate the problem by degrading today's GRACE data to a level comparable with SLR, then demonstrating that the inversion can re-localize Greenland's contribution to the low-resolution signal, giving an accurate time series of mass change over all of Greenland which compares well with the full-resolution GRACE estimates. I then utilize that method on the actual SLR data, resulting in an independent 1994-2014 time series of mass change over Greenland. I find favorable agreement between the pure-SLR inverted results and the 2012 Ice-sheet Mass Balance Inter-comparison Exercise (IMBIE) results, which are largely based on the "input-output" modeling method before GRACE's launch.
Free Vibration and Stability of Axially Functionally Graded Tapered Euler-Bernoulli Beams
Directory of Open Access Journals (Sweden)
Ahmad Shahba
2011-01-01
Full Text Available Structural analysis of axially functionally graded tapered Euler-Bernoulli beams is studied using finite element method. A beam element is proposed which takes advantage of the shape functions of homogeneous uniform beam elements. The effects of varying cross-sectional dimensions and mechanical properties of the functionally graded material are included in the evaluation of structural matrices. This method could be used for beam elements with any distributions of mass density and modulus of elasticity with arbitrarily varying cross-sectional area. Assuming polynomial distributions of modulus of elasticity and mass density, the competency of the element is examined in stability analysis, free longitudinal vibration and free transverse vibration of double tapered beams with different boundary conditions and the convergence rate of the element is then investigated.
Three dimensional steady subsonic Euler flows in bounded nozzles
Chen, Chao; Xie, Chunjing
The existence and uniqueness of three dimensional steady subsonic Euler flows in rectangular nozzles were obtained when prescribing normal component of momentum at both the entrance and exit. If, in addition, the normal component of the voriticity and the variation of Bernoulli's function at the entrance are both zero, then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number. As the magnitude of the normal component of the momentum approaches the critical number, the associated flows converge to a subsonic-sonic flow. Furthermore, when the normal component of vorticity and the variation of Bernoulli function are both small, the existence and uniqueness of subsonic Euler flows with non-zero vorticity are established. The proof of these results is based on a new formulation for the Euler system, a priori estimate for nonlinear elliptic equations with nonlinear boundary conditions, detailed study for a linear div-curl system, and delicate estimate for the transport equations.
Fractional Euler Limits and Their Applications
MacNamara, Shev; Henry, Bruce I; McLean, William
2016-01-01
Generalisations of the classical Euler formula to the setting of fractional calculus are discussed. Compound interest and fractional compound interest serve as motivation. Connections to fractional master equations are highlighted. An application to the Schlogl reactions with Mittag-Leffler waiting times is described.
Newton-Krylov methods applied to nonequilibrium radiation diffusion
International Nuclear Information System (INIS)
Knoll, D.A.; Rider, W.J.; Olsen, G.L.
1998-01-01
The authors present results of applying a matrix-free Newton-Krylov method to a nonequilibrium radiation diffusion problem. Here, there is no use of operator splitting, and Newton's method is used to convert the nonlinearities within a time step. Since the nonlinear residual is formed, it is used to monitor convergence. It is demonstrated that a simple Picard-based linearization produces a sufficient preconditioning matrix for the Krylov method, thus elevating the need to form or store a Jacobian matrix for Newton's method. They discuss the possibility that the Newton-Krylov approach may allow larger time steps, without loss of accuracy, as compared to an operator split approach where nonlinearities are not converged within a time step
Pinsker estimators for local helioseismology: inversion of travel times for mass-conserving flows
International Nuclear Information System (INIS)
Fournier, Damien; Holzke, Martin; Hohage, Thorsten; Gizon, Laurent
2016-01-01
A major goal of helioseismology is the three-dimensional reconstruction of the three velocity components of convective flows in the solar interior from sets of wave travel-time measurements. For small amplitude flows, the forward problem is described in good approximation by a large system of convolution equations. The input observations are highly noisy random vectors with a known dense covariance matrix. This leads to a large statistical linear inverse problem. Whereas for deterministic linear inverse problems several computationally efficient minimax optimal regularization methods exist, only one minimax-optimal linear estimator exists for statistical linear inverse problems: the Pinsker estimator. However, it is often computationally inefficient because it requires a singular value decomposition of the forward operator or it is not applicable because of an unknown noise covariance matrix, so it is rarely used for real-world problems. These limitations do not apply in helioseismology. We present a simplified proof of the optimality properties of the Pinsker estimator and show that it yields significantly better reconstructions than traditional inversion methods used in helioseismology, i.e. regularized least squares (Tikhonov regularization) and SOLA (approximate inverse) methods. Moreover, we discuss the incorporation of the mass conservation constraint in the Pinsker scheme using staggered grids. With this improvement we can reconstruct not only horizontal, but also vertical velocity components that are much smaller in amplitude. (paper)
Energy Technology Data Exchange (ETDEWEB)
Dellacherie, St. [CEA Saclay, Dir. de l' Energie Nucleaire DEN/SFNME/LMPE, Lab. de Modelisation Physique et de l' Enrichissement, 91 - Gif sur Yvette (France); Rency, N. [Paris-11 Univ., CNRS UMR 8628, 91 - Orsay (France)
2001-07-01
After having recalled the formal convergence of the semi-classical multi-species Boltzmann equations toward the multi-species Euler system (i.e. mixture of gases having the same velocity), we generalize to this system the closure relations proposed by B. Despres and by F. Lagoutiere for the multi-components Euler system (i.e. mixture of non miscible fluids having the same velocity). Then, we extend the energy relaxation schemes proposed by F. Coquel and by B. Perthame for the numerical resolution of the mono-species Euler system to the multi-species isothermal Euler system and to the multi-components isobar-isothermal Euler system. This allows to obtain a class of entropic schemes under a CFL criteria. In the multi-components case, this class of entropic schemes is perhaps a way for the treatment of interface problems and, then, for the treatment of the numerical mixture area by using a Lagrange + projection scheme. Nevertheless, we have to find a good projection stage in the multi-components case. At last, in the last chapter, we discuss, through the study of a dynamical system, about a system proposed by R. Abgrall and by R. Saurel for the numerical resolution of the multi-components Euler system.
Dakin, Gautier; Després, Bruno; Jaouen, Stéphane
2018-01-01
We propose a new high-order accurate numerical boundary treatment for solving hyperbolic systems of conservation laws and Euler equations using a Lagrange-remap approach on Cartesian grids in cases of physical boundaries not aligned with the mesh. The method is an adaptation of the Inverse Lax-Wendroff procedure [34-38] to the Lagrange-remap approach, which considerably alleviates the algebra. High-order accurate ghost values of conservative variables are imposed using Taylor expansions whose coefficients are found by inverting a (linear or non-linear) system which is well posed in all our examples. For 2D problems, a least-square procedure is added to prevent extrapolation instabilities. The Lagrange-remap formalism also provides a simpler fluid-structure coupling which is also described. Numerical examples are given for the linear case and Euler equations in 1D and 2D.
Kim, Ok-Hee; Cho, Yong-Hun; Kang, Soon Hyung; Park, Hee-Young; Kim, Minhyoung; Lim, Ju Wan; Chung, Dong Young; Lee, Myeong Jae; Choe, Heeman; Sung, Yung-Eun
2013-01-01
Three-dimensional, ordered macroporous materials such as inverse opal structures are attractive materials for various applications in electrochemical devices because of the benefits derived from their periodic structures: relatively large surface areas, large voidage, low tortuosity and interconnected macropores. However, a direct application of an inverse opal structure in membrane electrode assemblies has been considered impractical because of the limitations in fabrication routes including an unsuitable substrate. Here we report the demonstration of a single cell that maintains an inverse opal structure entirely within a membrane electrode assembly. Compared with the conventional catalyst slurry, an ink-based assembly, this modified assembly has a robust and integrated configuration of catalyst layers; therefore, the loss of catalyst particles can be minimized. Furthermore, the inverse-opal-structure electrode maintains an effective porosity, an enhanced performance, as well as an improved mass transfer and more effective water management, owing to its morphological advantages.
An inverse method for non linear ablative thermics with experimentation of automatic differentiation
Energy Technology Data Exchange (ETDEWEB)
Alestra, S [Simulation Information Technology and Systems Engineering, EADS IW Toulouse (France); Collinet, J [Re-entry Systems and Technologies, EADS ASTRIUM ST, Les Mureaux (France); Dubois, F [Professor of Applied Mathematics, Conservatoire National des Arts et Metiers Paris (France)], E-mail: stephane.alestra@eads.net, E-mail: jean.collinet@astrium.eads.net, E-mail: fdubois@cnam.fr
2008-11-01
Thermal Protection System is a key element for atmospheric re-entry missions of aerospace vehicles. The high level of heat fluxes encountered in such missions has a direct effect on mass balance of the heat shield. Consequently, the identification of heat fluxes is of great industrial interest but is in flight only available by indirect methods based on temperature measurements. This paper is concerned with inverse analyses of highly evolutive heat fluxes. An inverse problem is used to estimate transient surface heat fluxes (convection coefficient), for degradable thermal material (ablation and pyrolysis), by using time domain temperature measurements on thermal protection. The inverse problem is formulated as a minimization problem involving an objective functional, through an optimization loop. An optimal control formulation (Lagrangian, adjoint and gradient steepest descent method combined with quasi-Newton method computations) is then developed and applied, using Monopyro, a transient one-dimensional thermal model with one moving boundary (ablative surface) that has been developed since many years by ASTRIUM-ST. To compute numerically the adjoint and gradient quantities, for the inverse problem in heat convection coefficient, we have used both an analytical manual differentiation and an Automatic Differentiation (AD) engine tool, Tapenade, developed at INRIA Sophia-Antipolis by the TROPICS team. Several validation test cases, using synthetic temperature measurements are carried out, by applying the results of the inverse method with minimization algorithm. Accurate results of identification on high fluxes test cases, and good agreement for temperatures restitutions, are obtained, without and with ablation and pyrolysis, using bad fluxes initial guesses. First encouraging results with an automatic differentiation procedure are also presented in this paper.
Cooper, M.; Martin, R.; Henze, D. K.
2016-12-01
Nitrogen oxide (NOx ≡ NO + NO2) emission inventories can be improved through top-down constraints provided by inverse modeling of observed nitrogen dioxide (NO2) columns. Here we compare two methods of inverse modeling for emissions of NOx from synthetic NO2 columns generated from known emissions using the GEOS-Chem chemical transport model and its adjoint. We treat the adjoint-based 4D-VAR approach for estimating top-down emissions as a benchmark against which to evaluate variations on the mass balance method. We find that the standard mass balance algorithm can be improved by using an iterative process and using finite difference to calculate the local sensitivity of a change in NO2 columns to a change in emissions, resulting in a factor of two reduction in inversion error. In a simplified case study to recover local emission perturbations, horizontal smearing effects due to NOx transport were better resolved by the adjoint-based approach than by mass balance. For more complex emission changes that reflect real world scenarios, the iterative finite difference mass balance and adjoint methods produce similar top-down inventories when inverting hourly synthetic observations, both reducing the a priori error by factors of 3-4. Inversions of data sets that simulate satellite observations from low Earth and geostationary orbits also indicate that both the mass balance and adjoint inversions produce similar results, reducing a priori error by a factor of 3. As the iterative finite difference mass balance method provides similar accuracy as the adjoint-based 4D-VAR method, it offers the ability to efficiently estimate top-down emissions using models that do not have an adjoint.
Leonhard Euler's Wave Theory of Light
DEFF Research Database (Denmark)
Pedersen, Kurt Møller
2008-01-01
Euler's wave theory of light developed from a mere description of this notion based on an analogy between sound and light to a more and more mathematical elaboration on that notion. He was very successful in predicting the shape of achromatic lenses based on a new dispersion law that we now know...... of achromatic lenses, the explanation of colors of thin plates and of the opaque bodies as proof of his theory. When it came to the fundamental issues, the correctness of his dispersion law and the prediction of frequencies of light he was not at all successful. His wave theory degenerated, and it was not until...... is wrong. Most of his mathematical arguments were, however, guesswork without any solid physical reasoning. Guesswork is not always a bad thing in physics if it leads to new experiments or makes the theory coherent with other theories. And Euler tried to find such experiments. He saw the construction...
Chen, Kuan-Ting; Fan, Jun Wei; Chang, Shu-Tong; Lin, Chung-Yi
2015-03-01
In this paper, the subband structure and effective mass of an Si-based alloy inversion layer in a PMOSFET are studied theoretically. The strain condition considered in our calculations is the intrinsic strain resulting from growth of the silicon-carbon alloy on a (001) Si substrate and mechanical uniaxial stress. The quantum confinement effect resulting from the vertically effective electric field was incorporated into the k · p calculation. The distinct effective mass, such as the quantization effective mass and the density-of-states (DOS) effective mass, as well as the subband structure of the silicon-carbon alloy inversion layer for a PMOSFET under substrate strain and various effective electric field strengths, were all investigated. Ore results show that subband structure of relaxed silicon-carbon alloys with low carbon content are almost the same as silicon. We find that an external stress applied parallel to the channel direction can efficiently reduce the effective mass along the channel direction, thus producing hole mobility enhancement.
Conformal mechanics in Newton-Hooke spacetime
International Nuclear Information System (INIS)
Galajinsky, Anton
2010-01-01
Conformal many-body mechanics in Newton-Hooke spacetime is studied within the framework of the Lagrangian formalism. Global symmetries and Noether charges are given in a form convenient for analyzing the flat space limit. N=2 superconformal extension is built and a new class on N=2 models related to simple Lie algebras is presented. A decoupling similarity transformation on N=2 quantum mechanics in Newton-Hooke spacetime is discussed.
A new method for testing Newton's gravitational law
International Nuclear Information System (INIS)
Schurr, J.; Klein, N.; Meyer, H.; Piel, H.; Walesch, H.
1991-01-01
A new experimental method is reported for determining the gravitational force of a laboratory test mass on a Fabry-Perot microwave resonator. The resonator consists of two Fabry-Perot mirrors suspended as pendulums. Changes of 2·10 -11 m in the pendulum separation can be resolved as a shift of the resonance frequency of the resonator. This limit corresponds to an acceleration of 7·10 -11 m s -2 of one mirror with respect to the other. In a first experiment, the gravitational acceleration generated by a 125 kg test mass was measured as a function of distance in the range of 10 to 15 cm and tested Newton's gravitational law with an accuracy of 1%. No deviation is found. Furthermore, the gravitational constant G is determined with similar precision. (author) 5 refs., 2 figs
Lalov, E.; Linde, N.; Vrugt, J.A.
2012-01-01
Time-lapse geophysical measurements are widely used to monitor the movement of water and solutes through the subsurface. Yet commonly used deterministic least squares inversions typically suffer from relatively poor mass recovery, spread overestimation, and limited ability to appropriately estimate
Intra- and interobserver reliability of glenoid fracture classifications by Ideberg, Euler and AO.
Gilbert, F; Eden, L; Meffert, R; Konietschke, F; Lotz, J; Bauer, L; Staab, W
2018-03-27
Representing 3%-5% of shoulder girdle injuries scapula fractures are rare. Furthermore, approximately 1% of scapula fractures are intraarticularfractures of the glenoid fossa. Because of uncertain fracture morphology and limited experience, the treatment of glenoid fossa fractures is difficult. The glenoid fracture classification by Ideberg (1984) and Euler (1996) is still commonly used in literature. In 2013 a new glenoid fracture classification was introduced by the AO. The purpose of this study was to examine the new AO classification in clinical practice in comparison with the classifications by Ideberg and Euler. In total CT images of 84 patients with glenoid fossa fractures from 2005 to 2018 were included. Parasagittal, paracoronary and axial reconstructions were examined according to the classifications of Ideberg, Euler and the AO by 3 investigators (orthopedic surgeon, radiologist, student of medicine) at three individual time settings. Inter- and intraobserver reliability of the three classification systems were ascertained by computing Inter- and Intraclass (ICCs) correlation coefficients using Spearman's rank correlation coefficient, 95%-confidence intervals as well as F-tests for correlation coefficients. Inter- and intraobserver reliability for the AO classification showed a perspicuous coherence (R = 0.74 and R = 0.79). Low to moderate intraobserver reliability for Ideberg (R = 0.46) and Euler classification (R = 0.41) was found. Furthermore, data show a low Interobserver reliability for both Ideberg and Euler classification (R reliability using AO is significantly higher than those using Ideberg and Euler (p reliable grading of glenoid fossa fractures with high inter- and intraobserver reliability in 84 patients using CT images. It should possibly be applied in order to enable a valid, reliable and consistent academic description of glenoid fossa fractures. The established classifications by Euler and Ideberg are not capable of
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)
Newton's law of cooling revisited
International Nuclear Information System (INIS)
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 from any object to its surrounding is not only due to conduction and convection but also due to radiation. The latter does not vary linearly with temperature difference, which leads to deviations from Newton's law. This paper presents a theoretical analysis of the cooling of objects with a small Biot number. It is shown that Newton's law of cooling, i.e. simple exponential behaviour, is mostly valid if temperature differences are below a certain threshold which depends on the experimental conditions. For any larger temperature differences appreciable deviations occur which need the complete nonlinear treatment. This is demonstrated by results of some laboratory experiments which use IR imaging to measure surface temperatures of solid cooling objects with temperature differences of up to 300 K.
Isaac Newton and the astronomical refraction.
Lehn, Waldemar H
2008-12-01
In a short interval toward the end of 1694, Isaac Newton developed two mathematical models for the theory of the astronomical refraction and calculated two refraction tables, but did not publish his theory. Much effort has been expended, starting with Biot in 1836, in the attempt to identify the methods and equations that Newton used. In contrast to previous work, a closed form solution is identified for the refraction integral that reproduces the table for his first model (in which density decays linearly with elevation). The parameters of his second model, which includes the exponential variation of pressure in an isothermal atmosphere, have also been identified by reproducing his results. The implication is clear that in each case Newton had derived exactly the correct equations for the astronomical refraction; furthermore, he was the first to do so.
A Newton-Euler Description for Sediment Movement.
Maniatis, G.; Hoey, T.; Drysdale, T.; Hodge, R. A.; Valyrakis, M.
2015-12-01
We present progress from the development of a purpose specific sensing system for sediment transport (Maniatis et al. 2013). This system utilises the capabilities of contemporary inertial micro-sensors (strap-down accelerometers and gyroscopes) to record fluvial transport from the moving body-frame of artificial pebbles modelled precisely to represent the motion of real, coarse sediment grains (D90=100 mm class). This type of measurements can be useful in the context of sediment transport only if the existing mathematical understanding of the process is updated. We test a new mathematical model which defines specifically how the data recorded in the body frame of the sensor (Lagrangian frame of reference) can be generalised to the reference frame of the flow (channel, Eulerian frame of reference). Given the association of the two most widely used models for sediment transport with those frames of reference (Shields' to Eulerian frame and HA. Einstein's to Lagrangian frame), this description builds the basis for the definition of explicit incipient motion criteria (Maniatis et al. 2015) and for the upscaling from point-grain scale measurements to averaged, cross-sectional, stream related metrics. Flume experiments where conducted in the Hydraulics laboratory of the University of Glasgow where a spherical sensor of 800 mm diameter and capable of recoding inertial dynamics at 80Hz frequency was tested under fluvial transport conditions. We managed to measure the dynamical response of the unit during pre-entrainment/entrainment transitions, on scaled and non-scaled to the sensor's diameter bed and for a range of hydrodynamic conditions (slope up to 0.02 and flow increase rate up to 0.05m3.s-1. Preliminary results from field deployment on a mixed bedrock-alluvial channel are also presented. Maniatis et. al 2013 J. Sens. Actuator Netw. 2013, 2(4), 761-779; Maniatis et. al 2015: "CALCULATION OF EXPLICIT PROBABILITY OF ENTRAINMENT BASED ON INERTIAL ACCELERATION MEASUREMENTS" J. Hydraulic Engineering, Under review.
Sub-Millimeter Tests of the Newtonian Inverse Square Law
International Nuclear Information System (INIS)
Adelberger, Eric
2005-01-01
It is remarkable that small-scale experiments can address important open issues in fundamental science such as: 'why is gravity so weak compared to the other interactions?' and 'why is the cosmological constant so small compared to the predictions of quantum mechanics?' String theory ideas (new scalar particles and extra dimensions) and other notions hint that Newton's Inverse-Square Law could break down at distances less than 1 mm. I will review some motivations for testing the Inverse-Square Law, and discuss recent mechanical experiments with torsion balances, small-scillators, micro-cantilevers, and ultra-cold neutrons. Our torsion-balance experiments have probed for gravitational-strength interactions with length scales down to 70 micrometers, which is approximately the diameter of a human hair.
Inversion algorithms for large-scale geophysical electromagnetic measurements
International Nuclear Information System (INIS)
Abubakar, A; Habashy, T M; Li, M; Liu, J
2009-01-01
Low-frequency surface electromagnetic prospecting methods have been gaining a lot of interest because of their capabilities to directly detect hydrocarbon reservoirs and to compliment seismic measurements for geophysical exploration applications. There are two types of surface electromagnetic surveys. The first is an active measurement where we use an electric dipole source towed by a ship over an array of seafloor receivers. This measurement is called the controlled-source electromagnetic (CSEM) method. The second is the Magnetotelluric (MT) method driven by natural sources. This passive measurement also uses an array of seafloor receivers. Both surface electromagnetic methods measure electric and magnetic field vectors. In order to extract maximal information from these CSEM and MT data we employ a nonlinear inversion approach in their interpretation. We present two types of inversion approaches. The first approach is the so-called pixel-based inversion (PBI) algorithm. In this approach the investigation domain is subdivided into pixels, and by using an optimization process the conductivity distribution inside the domain is reconstructed. The optimization process uses the Gauss–Newton minimization scheme augmented with various forms of regularization. To automate the algorithm, the regularization term is incorporated using a multiplicative cost function. This PBI approach has demonstrated its ability to retrieve reasonably good conductivity images. However, the reconstructed boundaries and conductivity values of the imaged anomalies are usually not quantitatively resolved. Nevertheless, the PBI approach can provide useful information on the location, the shape and the conductivity of the hydrocarbon reservoir. The second method is the so-called model-based inversion (MBI) algorithm, which uses a priori information on the geometry to reduce the number of unknown parameters and to improve the quality of the reconstructed conductivity image. This MBI approach can
A New Euler's Formula for DNA Polyhedra
Hu, Guang; Qiu, Wen-Yuan; Ceulemans, Arnout
2011-01-01
DNA polyhedra are cage-like architectures based on interlocked and interlinked DNA strands. We propose a formula which unites the basic features of these entangled structures. It is based on the transformation of the DNA polyhedral links into Seifert surfaces, which removes all knots. The numbers of components , of crossings , and of Seifert circles are related by a simple and elegant formula: . This formula connects the topological aspects of the DNA cage to the Euler characteristic of the underlying polyhedron. It implies that Seifert circles can be used as effective topological indices to describe polyhedral links. Our study demonstrates that, the new Euler's formula provides a theoretical framework for the stereo-chemistry of DNA polyhedra, which can characterize enzymatic transformations of DNA and be used to characterize and design novel cages with higher genus. PMID:22022596
Workflows for Full Waveform Inversions
Boehm, Christian; Krischer, Lion; Afanasiev, Michael; van Driel, Martin; May, Dave A.; Rietmann, Max; Fichtner, Andreas
2017-04-01
Despite many theoretical advances and the increasing availability of high-performance computing clusters, full seismic waveform inversions still face considerable challenges regarding data and workflow management. While the community has access to solvers which can harness modern heterogeneous computing architectures, the computational bottleneck has fallen to these often manpower-bounded issues that need to be overcome to facilitate further progress. Modern inversions involve huge amounts of data and require a tight integration between numerical PDE solvers, data acquisition and processing systems, nonlinear optimization libraries, and job orchestration frameworks. To this end we created a set of libraries and applications revolving around Salvus (http://salvus.io), a novel software package designed to solve large-scale full waveform inverse problems. This presentation focuses on solving passive source seismic full waveform inversions from local to global scales with Salvus. We discuss (i) design choices for the aforementioned components required for full waveform modeling and inversion, (ii) their implementation in the Salvus framework, and (iii) how it is all tied together by a usable workflow system. We combine state-of-the-art algorithms ranging from high-order finite-element solutions of the wave equation to quasi-Newton optimization algorithms using trust-region methods that can handle inexact derivatives. All is steered by an automated interactive graph-based workflow framework capable of orchestrating all necessary pieces. This naturally facilitates the creation of new Earth models and hopefully sparks new scientific insights. Additionally, and even more importantly, it enhances reproducibility and reliability of the final results.
Euler-Poincare Reduction of Externall Forced Rigid Body Motion
DEFF Research Database (Denmark)
Wisniewski, Rafal; Kulczycki, P.
2004-01-01
If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action....... Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems......-known Euler-Poincaré reduction to a rigid body motion with forcing....
Euler-Poincaré Reduction of a Rigid Body Motion
DEFF Research Database (Denmark)
Wisniewski, Rafal; Kulczycki, P.
2004-01-01
If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action....... Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems......-known Euler-Poincaré reduction to a rigid body motion with forcing....
Newton slopes for Artin-Schreier-Witt towers
DEFF Research Database (Denmark)
Davis, Christopher; Wan, Daqing; Xiao, Liang
2016-01-01
We fix a monic polynomial f(x)∈Fq[x] over a finite field and consider the Artin-Schreier-Witt tower defined by f(x); this is a tower of curves ⋯→Cm→Cm−1→⋯→C0=A1, with total Galois group Zp. We study the Newton slopes of zeta functions of this tower of curves. This reduces to the study of the Newton...... slopes of L-functions associated to characters of the Galois group of this tower. We prove that, when the conductor of the character is large enough, the Newton slopes of the L-function form arithmetic progressions which are independent of the conductor of the character. As a corollary, we obtain...
On the topology of the Newton boundary at infinity
International Nuclear Information System (INIS)
Pham Tien Son
2007-07-01
We will be interested in a global version of Le-Ramanujam μ -constant theorem from the Newton polyhedron point of view. More precisely, we prove a stability theorem which says that the global monodromy fibration of a polynomial with Newton non-degenerate is uniquely determined by its Newton boundary at infinity. Besides, the continuity of atypical values for a family of complex polynomial functions also is considered. (author)
Exploitation of ISAR Imagery in Euler Parameter Space
National Research Council Canada - National Science Library
Baird, Christopher; Kersey, W. T; Giles, R; Nixon, W. E
2005-01-01
.... The Euler parameters have potential value in target classification but have historically met with limited success due to ambiguities that arise in decomposition as well as the parameters' sensitivity...
Classical Monopoles: Newton, NUT-space, gravomagnetic lensing and atomic spectra
Lynden-Bell, Donald; Nouri-Zonoz, Mohammad
1996-01-01
Stimulated by a scholium in Newton's Principia we find some beautiful results in classical mechanics which can be interpreted in terms of the orbits in the field of a mass endowed with a gravomagnetic monopole. All the orbits lie on cones! When the cones are slit open and flattened the orbits are exactly the ellipses and hyperbolae that one would have obtained without the gravomagnetic monopole. The beauty and simplicity of these results has led us to explore the similar problems in Atomic Ph...
An inverse Sturm–Liouville problem with a fractional derivative
Jin, Bangti
2012-05-01
In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and numerical reconstructions of the potential with a Newton method from finite spectral data are presented. Surprisingly, it allows very satisfactory reconstructions for both smooth and discontinuous potentials, provided that the order . α∈. (1,. 2) of fractional derivative is sufficiently away from 2. © 2012 Elsevier Inc.
Guo, H. Y.; Li, Y. Q.; Wu, K.; Wang, S. K.
2001-01-01
We study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncomutative differential geometry. By virtue of this variational principle, we get the difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical mechanics and classical field theory. We also explore the difference discrete versions for the Euler...
Analysis of Damped Mass-Spring Systems for Sound Synthesis
Directory of Open Access Journals (Sweden)
Don Morgan
2009-01-01
Full Text Available There are many ways of synthesizing sound on a computer. The method that we consider, called a mass-spring system, synthesizes sound by simulating the vibrations of a network of interconnected masses, springs, and dampers. Numerical methods are required to approximate the differential equation of a mass-spring system. The standard numerical method used in implementing mass-spring systems for use in sound synthesis is the symplectic Euler method. Implementers and users of mass-spring systems should be aware of the limitations of the numerical methods used; in particular we are interested in the stability and accuracy of the numerical methods used. We present an analysis of the symplectic Euler method that shows the conditions under which the method is stable and the accuracy of the decay rates and frequencies of the sounds produced.
Verlet, Loup
1993-01-01
En 1936, une vente publique ramena au jour le contenu d'une malle où Newton avait enfermé ses manuscrits. Ô surprise, les travaux du savant y voisinaient avec les spéculations de l'exégète et de l'alchimiste. Ce n'est pas seulement la face cachée d'un exceptionnel génie scientifique qui nous était ainsi révélée, mais, au-delà du mystère d'un homme, le secret partage qui gouverne notre univers, comme le montre cette lecture originale de la naissance de la physique moderne.Dans quel monde suis-je tombé ? Pourquoi les choses sont-elles ainsi ? Comment faire avec ? Questions lancinantes de l'enfant quand la mère fait défaut, du chercheur face à la nature qui se dérobe. La réponse, Newton sait où la trouver : Dieu le Père, à jamais insaisissable, est présent «partout et toujours», Il se révèle par la bouche des prophètes, se devine dans les arcanes de l'alchimie, se manifeste par les lois admirables qui règlent le cours ordinaire des choses. Ses écrits de l'ombre l'attestent, Newton ...
Voltaire-Newton... Renversant!
2004-01-01
The encounter, even improbable, between François Marie Arouet, said Voltaire, and Isaac Newton could occur only in Pays de Gex, near his city... It's indeed right above of the accelerator, in Saint-Genis, that the meeting between this two "monsters" of the 18e century took place
DEFF Research Database (Denmark)
Souza, A.; Santos, Ilmar
2002-01-01
dynamics is led with help of a set of non-linear equations of motion obtained using Newton-Euler-Jourdain´s Method. Such a set of equation is numerically solved and the theoretical results are compared with experimental carried out with a laboratory prototype. Comparisons show that the theoretical model...... predicts well the mechanism movements. However it was also experimentally observed that the contact between the wheels and the road profile is not permanent. To analyze the non-contact between the wheels and the road, the Newton-Euler´s Method is used to calculate forces and moments of reactions between...
Iterative Reconstruction Methods for Hybrid Inverse Problems in Impedance Tomography
DEFF Research Database (Denmark)
Hoffmann, Kristoffer; Knudsen, Kim
2014-01-01
For a general formulation of hybrid inverse problems in impedance tomography the Picard and Newton iterative schemes are adapted and four iterative reconstruction algorithms are developed. The general problem formulation includes several existing hybrid imaging modalities such as current density...... impedance imaging, magnetic resonance electrical impedance tomography, and ultrasound modulated electrical impedance tomography, and the unified approach to the reconstruction problem encompasses several algorithms suggested in the literature. The four proposed algorithms are implemented numerically in two...
Neutrino Masses with Inverse Hierarchy from Broken $L_{e}-L_{\\mu}-L_{\\tau}$: a Reappraisal
Altarelli, Guido; Altarelli, Guido; Franceschini, Roberto
2006-01-01
We discuss a class of models of neutrino masses and mixings with inverse hierarchy based on a broken U(1)_F flavour symmetry with charge L_e-L_\\mu-L_\\tau. The symmetry breaking sector receives separate contributions from flavon vev breaking terms and from soft mass breaking in the right handed Majorana sector. The model is able to reproduce in a natural way all observed features of the charged lepton mass spectrum and of neutrino masses and mixings (even with arbitrarily small \\theta_{13}), with the exception of a moderate fine tuning which is needed to accomodate the observed small value of r = Delta m^2_{sol} / Delta m^2_{atm}.
Newton's law in braneworlds with an infinite extra dimension
Ito, Masato
2001-01-01
We study the behavior of the four$-$dimensional Newton's law in warped braneworlds. The setup considered here is a $(3+n)$-brane embedded in $(5+n)$ dimensions, where $n$ extra dimensions are compactified and a dimension is infinite. We show that the wave function of gravity is described in terms of the Bessel functions of $(2+n/2)$-order and that estimate the correction to Newton's law. In particular, the Newton's law for $n=1$ can be exactly obtained.
Hukum Newton Tentang Gerak Dalam Ruang Fase Tak Komutatif
Purwanto, Joko
2014-01-01
In this paper, the Newton's law of motions in a noncomutative phase space has been investigated. Its show that correction to the Newton's first and second law appear if we assume that the phase space has symplectic structure consistent with the rules of comutation of the noncomutative quantum mechanics. In the free particle and harmonic oscillator case the equations of motion are derived on basis of the modified Newton's second law in a noncomutative phase space.
Maiti, Soumyabrata; Bandyopadhyay, Ritwik; Chatterjee, Anindya
2018-01-01
We study free and harmonically forced vibrations of an Euler-Bernoulli beam with rate-independent hysteretic dissipation. The dissipation follows a model proposed elsewhere for materials with randomly dispersed frictional microcracks. The virtual work of distributed dissipative moments is approximated using Gaussian quadrature, yielding a few discrete internal hysteretic states. Lagrange's equations are obtained for the modal coordinates. Differential equations for the modal coordinates and internal states are integrated together. Free vibrations decay exponentially when a single mode dominates. With multiple modes active, higher modes initially decay rapidly while lower modes decay relatively slowly. Subsequently, lower modes show their own characteristic modal damping, while small amplitude higher modes show more erratic decay. Large dissipation, for the adopted model, leads mathematically to fast and damped oscillations in the limit, unlike viscously overdamped systems. Next, harmonically forced, lightly damped responses of the beam are studied using both a slow frequency sweep and a shooting-method based search for periodic solutions along with numerical continuation. Shooting method and frequency sweep results match for large ranges of frequency. The shooting method struggles near resonances, where internal states collapse into lower dimensional behavior and Newton-Raphson iterations fail. Near the primary resonances, simple numerically-aided harmonic balance gives excellent results. Insights are also obtained into the harmonic content of secondary resonances.
Newton and the origin of civilization
Buchwald, Jed Z
2012-01-01
Isaac Newton's Chronology of Ancient Kingdoms Amended, published in 1728, one year after the great man's death, unleashed a storm of controversy. And for good reason. The book presents a drastically revised timeline for ancient civilizations, contracting Greek history by five hundred years and Egypt's by a millennium. Newton and the Origin of Civilization tells the story of how one of the most celebrated figures in the history of mathematics, optics, and mechanics came to apply his unique ways of thinking to problems of history, theology, and mythology, and of how his radical ideas produced an uproar that reverberated in Europe's learned circles throughout the eighteenth century and beyond. Jed Buchwald and Mordechai Feingold reveal the manner in which Newton strove for nearly half a century to rectify universal history by reading ancient texts through the lens of astronomy, and to create a tight theoretical system for interpreting the evolution of civilization on the basis of population dynamics. It was duri...
International Nuclear Information System (INIS)
Bahar, M.K.; Yasuk, F.
2013-01-01
Approximate solutions of the Dirac equation with positron-dependent mass are presented for the inversely quadratic Yukawa potential and Coulomb-like tensor interaction by using the asymptotic iteration method. The energy eigenvalues and the corresponding normalized eigenfunctions are obtained in the case of positron-dependent mass and arbitrary spin-orbit quantum number k state and approximation on the spin-orbit coupling term. (author)
Some Elementary Examples from Newton's Principia -R-ES ...
Indian Academy of Sciences (India)
ing both differential and integral calculus. Newton used many geometrical methods extensively to derive the re- sults in spite of his having discovered calculus. Geome- try, judiciously used with limiting procedures, was one principal strategy used by Newton in the Principia. The Principia presents an enormous range of ...
XMM-Newton On-demand Reprocessing Using SaaS Technology
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.
Inversion interpretation of the mise-a-la-masse data; Denryu den`i ho data no inversion kaiseki
Energy Technology Data Exchange (ETDEWEB)
Okuno, M; Hatanaka, H; Mizunaga, H; Ushijima, K [Kyushu University, Fukuoka (Japan). Faculty of Engineering
1996-05-01
A program was developed for the inversion interpretation of the mise-a-la-masse data, and was applied to a numerical model experiment and to the study of data obtained by actual probing. For the development of this program, a program was used that calculated by finite difference approximation the potential produced by a linear current source, and studies were made through forward interpretation, inversion interpretation of the acquired apparent resistivity data, comparison with the true solution, accuracy and tendency, and the limitations. In the simulation of a horizontal 2-layer model, the parametric value after 20 repetitions converged with deviation of 1% or lower. This program was applied to the data from probing the Hatchobara district, Oita Prefecture, using a model wherein the target area was divided into 5 from east to west, and into 2 in the direction of depth. The result suggested that there was a large-scale low-resistivity body deep in the ground in the southeastern part of the investigated area. Furthermore, there was a spot detected in the direction of east-northeast that suggested an electric structure continuous in the direction of depth and a fault-like structure discontinuous in the transverse direction. 7 refs., 9 figs.
Directory of Open Access Journals (Sweden)
Min Chen
2014-01-01
Full Text Available We study the one-dimensional bipolar nonisentropic Euler-Poisson equations which can model various physical phenomena, such as the propagation of electron and hole in submicron semiconductor devices, the propagation of positive ion and negative ion in plasmas, and the biological transport of ions for channel proteins. We show the existence and large time behavior of global smooth solutions for the initial value problem, when the difference of two particles’ initial mass is nonzero, and the far field of two particles’ initial temperatures is not the ambient device temperature. This result improves that of Y.-P. Li, for the case that the difference of two particles’ initial mass is zero, and the far field of the initial temperature is the ambient device temperature.
Mang, Andreas; Ruthotto, Lars
2017-01-01
We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic Metric Mappings (LDDMM). We use an optimal control formulation, in which the velocity field of a hyperbolic PDE needs to be found such that the distance between the final state of the system (the transformed/transported template image) and the observation (the reference image) is minimized. Our solver supports both stationary and non-stationary (i.e., transient or time-dependent) velocity fields. As transformation models, we consider both the transport equation (assuming intensities are preserved during the deformation) and the continuity equation (assuming mass-preservation). We consider the reduced form of the optimal control problem and solve the resulting unconstrained optimization problem using a discretize-then-optimize approach. A key contribution is the elimination of the PDE constraint using a Lagrangian hyperbolic PDE solver. Lagrangian methods rely on the concept of characteristic curves. We approximate these curves using a fourth-order Runge-Kutta method. We also present an efficient algorithm for computing the derivatives of the final state of the system with respect to the velocity field. This allows us to use fast Gauss-Newton based methods. We present quickly converging iterative linear solvers using spectral preconditioners that render the overall optimization efficient and scalable. Our method is embedded into the image registration framework FAIR and, thus, supports the most commonly used similarity measures and regularization functionals. We demonstrate the potential of our new approach using several synthetic and real world test problems with up to 14.7 million degrees of freedom.
Newton's Contributions to Optics
Indian Academy of Sciences (India)
creativity is apparent, even in ideas and models in optics that were ... Around Newton's time, a number of leading figures in science ..... successive circles increased as integers, i.e. d increases by inte- ... of easy reflections and transmission".
A stochastic Galerkin method for the Euler equations with Roe variable transformation
Pettersson, Per; Iaccarino, Gianluca; Nordströ m, Jan
2014-01-01
The Euler equations subject to uncertainty in the initial and boundary conditions are investigated via the stochastic Galerkin approach. We present a new fully intrusive method based on a variable transformation of the continuous equations. Roe variables are employed to get quadratic dependence in the flux function and a well-defined Roe average matrix that can be determined without matrix inversion.In previous formulations based on generalized polynomial chaos expansion of the physical variables, the need to introduce stochastic expansions of inverse quantities, or square roots of stochastic quantities of interest, adds to the number of possible different ways to approximate the original stochastic problem. We present a method where the square roots occur in the choice of variables, resulting in an unambiguous problem formulation.The Roe formulation saves computational cost compared to the formulation based on expansion of conservative variables. Moreover, the Roe formulation is more robust and can handle cases of supersonic flow, for which the conservative variable formulation fails to produce a bounded solution. For certain stochastic basis functions, the proposed method can be made more effective and well-conditioned. This leads to increased robustness for both choices of variables. We use a multi-wavelet basis that can be chosen to include a large number of resolution levels to handle more extreme cases (e.g. strong discontinuities) in a robust way. For smooth cases, the order of the polynomial representation can be increased for increased accuracy. © 2013 Elsevier Inc.
Micro-orbits in a many-brane model and deviations from Newton's 1/r^2 law
Donini, A.; Marimón, S. G.
2016-12-01
We consider a five-dimensional model with geometry M = M_4 × S_1, with compactification radius R. The Standard Model particles are localized on a brane located at y=0, with identical branes localized at different points in the extra dimension. Objects located on our brane can orbit around objects located on a brane at a distance d=y/R, with an orbit and a period significantly different from the standard Newtonian ones. We study the kinematical properties of the orbits, finding that it is possible to distinguish one motion from the other in a large region of the initial conditions parameter space. This is a warm-up to study if a SM-like mass distribution on one (or more) distant brane(s) may represent a possible dark matter candidate. After using the same technique to the study of orbits of objects lying on the same brane (d=0), we apply this method to the detection of generic deviations from the inverse-square Newton law. We propose a possible experimental setup to look for departures from Newtonian motion in the micro-world, finding that an order of magnitude improvement on present bounds can be attained at the 95% CL under reasonable assumptions.
Micro-orbits in a many-brane model and deviations from Newton's 1/r"2 law
International Nuclear Information System (INIS)
Donini, A.; Marimon, S.G.
2016-01-01
We consider a five-dimensional model with geometry M = M_4 x S_1, with compactification radius R. The Standard Model particles are localized on a brane located at y = 0, with identical branes localized at different points in the extra dimension. Objects located on our brane can orbit around objects located on a brane at a distance d = y/R, with an orbit and a period significantly different from the standard Newtonian ones. We study the kinematical properties of the orbits, finding that it is possible to distinguish one motion from the other in a large region of the initial conditions parameter space. This is a warm-up to study if a SM-like mass distribution on one (or more) distant brane(s) may represent a possible dark matter candidate. After using the same technique to the study of orbits of objects lying on the same brane (d = 0), we apply this method to the detection of generic deviations from the inverse-square Newton law. We propose a possible experimental setup to look for departures from Newtonian motion in the micro-world, finding that an order of magnitude improvement on present bounds can be attained at the 95% CL under reasonable assumptions. (orig.)
Photon and graviton mass limits
Energy Technology Data Exchange (ETDEWEB)
Nieto, Michael [Los Alamos National Laboratory; Goldhaber Scharff, Alfred [SUNY
2008-01-01
We review past and current studies of possible long-distance, low-frequency deviations from Maxwell electrodynamics and Einstein gravity. Both have passed through three phases: (1) Testing the inverse-square laws of Newton and Coulomb, (2) Seeking a nonzero value for the rest mass of photon or graviton, and (3) Considering more degrees of freedom, allowing mass while preserving gauge or general-coordinate invariance. For electrodynamics there continues to be no sign of any deviation. Since our previous review the lower limit on the photon Compton wavelength (associated with weakening of electromagnetic fields in vacuum over large distance scale) has improved by four orders of magnitude, to about one astronomical unit. Rapid current progress in astronomical observations makes it likely that there will be further advances. These ultimately could yield a bound exceeding galactic dimensions, as has long been contemplated. Meanwhile, for gravity there have been strong arguments about even the concept of a graviton rest mass. At the same time there are striking observations, commonly labeled 'dark matter' and 'dark energy' that some argue imply modified gravity. This makes the questions for gravity much more interesting. For dark matter, which involves increased attraction at large distances, any explanation by modified gravity would be qualitatively different from graviton mass. Because dark energy is associated with reduced attraction at large distances, it might be explained by a graviton-mass-like effect.
Palatnik, Dmitriy
2002-01-01
In this note one suggests a possibility of direct observation of the $\\theta$-parameter, introduced in the Born--Infeld theory of electroweak and gravitational fields, developed in quant-ph/0202024. Namely, one may treat $\\theta$ as a universal constant, responsible for correction to the Coulomb and Newton laws, allowing direct interaction between electrical charges and masses.
Disformal transformation in Newton-Cartan geometry
Energy Technology Data Exchange (ETDEWEB)
Huang, Peng [Zhejiang Chinese Medical University, Department of Information, Hangzhou (China); Sun Yat-Sen University, School of Physics and Astronomy, Guangzhou (China); Yuan, Fang-Fang [Nankai University, School of Physics, Tianjin (China)
2016-08-15
Newton-Cartan geometry has played a central role in recent discussions of the non-relativistic holography and condensed matter systems. Although the conformal transformation in non-relativistic holography can easily be rephrased in terms of Newton-Cartan geometry, we show that it requires a nontrivial procedure to arrive at the consistent form of anisotropic disformal transformation in this geometry. Furthermore, as an application of the newly obtained transformation, we use it to induce a geometric structure which may be seen as a particular non-relativistic version of the Weyl integrable geometry. (orig.)
Bargmann structures and Newton-Cartan theory
International Nuclear Information System (INIS)
Duval, C.; Burdet, G.; Kuenzle, H.P.; Perrin, M.
1985-01-01
It is shown that Newton-Cartan theory of gravitation can best be formulated on a five-dimensional extended space-time carrying a Lorentz metric together with a null parallel vector field. The corresponding geometry associated with the Bargmann group (nontrivially extended Galilei group) viewed as a subgroup of the affine de Sitter group AO(4,1) is thoroughly investigated. This new global formalism allows one to recast classical particle dynamics and the Schroedinger equation into a purely covariant form. The Newton-Cartan field equations are readily derived from Einstein's Lagrangian on the space-time extension
2000-02-01
many years of work. They are all that we hoped they would be. In the LMC we can see the elements, which go to make up new stars and planets, being released in giant stellar explosions. We can even see the creation of new stars going on, using elements scattered through space by previous stellar explosions. This is what we built the EPIC cameras for and they are really fulfilling their promise" Multiwavelength views of Hickson Group 16 The HCG-16 viewed by EPIC and by the Optical Monitor in the visible and ultraviolet wavelengths is one of approximately a hundred compact galaxy clusters listed by Canadian astronomer Paul Hickson in the 1980s. The criteria for the Hickson cluster groups included their compactness, their isolation from other galaxies and a limited magnitude range between their members. Most Hicksons are very faint, but a few can be observed with modest aperture telescopes. Galaxies in Hickson groups have a high probability of interacting. Their study has shed light on the question of galactic evolution and the effects of interaction. Investigation into their gravitational behaviour has also significantly contributed to our understanding of "dark matter", the mysterious matter that most astronomers feel comprises well over 90% of our universe. Observation of celestial objects from space over a range of X-ray, ultraviolet and visible wavelengths, is a unique feature of the XMM-Newton mission. The EPIC-PN view of the Hickson 16 group shows a handful of bright X-sources and in the background more than a hundred faint X-ray sources that XMM-Newton is revealing for the first time. Juxtaposing the X-ray view of HCG 16 with that of the Optical Monitor reveals one of the great strengths of XMM-Newton in being able to routinely compare the optical, ultraviolet and X-ray properties of objects. Many of the X-ray sources are revealed as elongated "fuzzy blobs" coincident with some of the optical galaxies. Routine access to ultraviolet images is a first for the mission
eulerAPE: drawing area-proportional 3-Venn diagrams using ellipses.
Micallef, Luana; Rodgers, Peter
2014-01-01
Venn diagrams with three curves are used extensively in various medical and scientific disciplines to visualize relationships between data sets and facilitate data analysis. The area of the regions formed by the overlapping curves is often directly proportional to the cardinality of the depicted set relation or any other related quantitative data. Drawing these diagrams manually is difficult and current automatic drawing methods do not always produce appropriate diagrams. Most methods depict the data sets as circles, as they perceptually pop out as complete distinct objects due to their smoothness and regularity. However, circles cannot draw accurate diagrams for most 3-set data and so the generated diagrams often have misleading region areas. Other methods use polygons to draw accurate diagrams. However, polygons are non-smooth and non-symmetric, so the curves are not easily distinguishable and the diagrams are difficult to comprehend. Ellipses are more flexible than circles and are similarly smooth, but none of the current automatic drawing methods use ellipses. We present eulerAPE as the first method and software that uses ellipses for automatically drawing accurate area-proportional Venn diagrams for 3-set data. We describe the drawing method adopted by eulerAPE and we discuss our evaluation of the effectiveness of eulerAPE and ellipses for drawing random 3-set data. We compare eulerAPE and various other methods that are currently available and we discuss differences between their generated diagrams in terms of accuracy and ease of understanding for real world data.
eulerAPE: drawing area-proportional 3-Venn diagrams using ellipses.
Directory of Open Access Journals (Sweden)
Luana Micallef
Full Text Available Venn diagrams with three curves are used extensively in various medical and scientific disciplines to visualize relationships between data sets and facilitate data analysis. The area of the regions formed by the overlapping curves is often directly proportional to the cardinality of the depicted set relation or any other related quantitative data. Drawing these diagrams manually is difficult and current automatic drawing methods do not always produce appropriate diagrams. Most methods depict the data sets as circles, as they perceptually pop out as complete distinct objects due to their smoothness and regularity. However, circles cannot draw accurate diagrams for most 3-set data and so the generated diagrams often have misleading region areas. Other methods use polygons to draw accurate diagrams. However, polygons are non-smooth and non-symmetric, so the curves are not easily distinguishable and the diagrams are difficult to comprehend. Ellipses are more flexible than circles and are similarly smooth, but none of the current automatic drawing methods use ellipses. We present eulerAPE as the first method and software that uses ellipses for automatically drawing accurate area-proportional Venn diagrams for 3-set data. We describe the drawing method adopted by eulerAPE and we discuss our evaluation of the effectiveness of eulerAPE and ellipses for drawing random 3-set data. We compare eulerAPE and various other methods that are currently available and we discuss differences between their generated diagrams in terms of accuracy and ease of understanding for real world data.
Euler's fluid equations: Optimal control vs optimization
Energy Technology Data Exchange (ETDEWEB)
Holm, Darryl D., E-mail: d.holm@ic.ac.u [Department of Mathematics, Imperial College London, SW7 2AZ (United Kingdom)
2009-11-23
An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the Eulerian velocity vector field. Thus, an optimal control problem and an optimization problem for incompressible ideal fluid flow both yield the same Euler fluid equations, although their Lagrangian parcel dynamics are different. This is a result of the gauge freedom in the definition of the fluid pressure for an incompressible flow, in combination with the symmetry of fluid dynamics under relabeling of their Lagrangian coordinates. Similar ideas are also illustrated for SO(N) rigid body motion.
Czech Academy of Sciences Publication Activity Database
Axelsson, Owe; Sysala, Stanislav
2015-01-01
Roč. 70, č. 11 (2015), s. 2621-2637 ISSN 0898-1221 R&D Projects: GA ČR GA13-18652S Institutional support: RVO:68145535 Keywords : system of nonlinear equations * Newton method * load increment method * elastoplasticity Subject RIV: IN - Informatics, Computer Science Impact factor: 1.398, year: 2015 http://www.sciencedirect.com/science/article/pii/S0898122115003818
2008-01-01
Isaac Newton, besides being the founder of modern physics, was also master of Britain's mint. That is a precedent which many British physicists must surely wish had become traditional. At the moment, money for physics is in short supply in Britain.
Discretization vs. Rounding Error in Euler's Method
Borges, Carlos F.
2011-01-01
Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…
Euler Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2012-01-01
Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....
Newton force from wave function collapse: speculation and test
International Nuclear Information System (INIS)
Diósi, Lajos
2014-01-01
The Diosi-Penrose model of quantum-classical boundary postulates gravity-related spontaneous wave function collapse of massive degrees of freedom. The decoherence effects of the collapses are in principle detectable if not masked by the overwhelming environmental decoherence. But the DP (or any other, like GRW, CSL) spontaneous collapses are not detectable themselves, they are merely the redundant formalism of spontaneous decoherence. To let DP collapses become testable physics, recently we extended the DP model and proposed that DP collapses are responsible for the emergence of the Newton gravitational force between massive objects. We identified the collapse rate, possibly of the order of 1/ms, with the rate of emergence of the Newton force. A simple heuristic emergence (delay) time was added to the Newton law of gravity. This non-relativistic delay is in peaceful coexistence with Einstein's relativistic theory of gravitation, at least no experimental evidence has so far surfaced against it. We derive new predictions of such a 'lazy' Newton law that will enable decisive laboratory tests with available technologies. The simple equation of 'lazy' Newton law deserves theoretical and experimental studies in itself, independently of the underlying quantum foundational considerations.
One biquaternion model of electro-gravimagnetic field. Field analogues of Newton laws
Alexeyeva, Lyudmila A.
2007-01-01
Using the biquaternions algebra with involution and mutual quaternional gradients the equations of one model of electro-gravimagnetic (EGM) field are constructed on the base of Hamilton form of Maxwell equations. For this field the hypothesis of equivalence of magnetic charge to gravitational mass is implied. The equations of interaction of generated by different charges and currents EGM-fields are built. On its base the analogies of three Newton's laws are obtained. The laws of transformatio...
Euler-Poincaré Reduction of Externally Forced Rigid Body Motion
DEFF Research Database (Denmark)
Wisniewski, Rafal; Kulczycki, P.
2004-01-01
If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action....... Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems......-known Euler-Poincaré reduction to a rigid body motion with forcing....
2.5D Inversion Algorithm of Frequency-Domain Airborne Electromagnetics with Topography
Directory of Open Access Journals (Sweden)
Jianjun Xi
2016-01-01
Full Text Available We presented a 2.5D inversion algorithm with topography for frequency-domain airborne electromagnetic data. The forward modeling is based on edge finite element method and uses the irregular hexahedron to adapt the topography. The electric and magnetic fields are split into primary (background and secondary (scattered field to eliminate the source singularity. For the multisources of frequency-domain airborne electromagnetic method, we use the large-scale sparse matrix parallel shared memory direct solver PARDISO to solve the linear system of equations efficiently. The inversion algorithm is based on Gauss-Newton method, which has the efficient convergence rate. The Jacobian matrix is calculated by “adjoint forward modelling” efficiently. The synthetic inversion examples indicated that our proposed method is correct and effective. Furthermore, ignoring the topography effect can lead to incorrect results and interpretations.
Cavitation Modeling in Euler and Navier-Stokes Codes
Deshpande, Manish; Feng, Jinzhang; Merkle, Charles L.
1993-01-01
Many previous researchers have modeled sheet cavitation by means of a constant pressure solution in the cavity region coupled with a velocity potential formulation for the outer flow. The present paper discusses the issues involved in extending these cavitation models to Euler or Navier-Stokes codes. The approach taken is to start from a velocity potential model to ensure our results are compatible with those of previous researchers and available experimental data, and then to implement this model in both Euler and Navier-Stokes codes. The model is then augmented in the Navier-Stokes code by the inclusion of the energy equation which allows the effect of subcooling in the vicinity of the cavity interface to be modeled to take into account the experimentally observed reduction in cavity pressures that occurs in cryogenic fluids such as liquid hydrogen. Although our goal is to assess the practicality of implementing these cavitation models in existing three-dimensional, turbomachinery codes, the emphasis in the present paper will center on two-dimensional computations, most specifically isolated airfoils and cascades. Comparisons between velocity potential, Euler and Navier-Stokes implementations indicate they all produce consistent predictions. Comparisons with experimental results also indicate that the predictions are qualitatively correct and give a reasonable first estimate of sheet cavitation effects in both cryogenic and non-cryogenic fluids. The impact on CPU time and the code modifications required suggests that these models are appropriate for incorporation in current generation turbomachinery codes.
INVESTIGATION OF THE MISCONCEPTION IN NEWTON II LAW
Directory of Open Access Journals (Sweden)
Yudi Kurniawan
2018-04-01
Full Text Available This study aims to provide a comprehensive description of the level of the number of students who have misconceptions about Newton's II Law. This research is located at one State Junior High School in Kab. Pandeglang. The purposive sampling was considering used in this study because it is important to distinguish students who do not know the concept of students who experience misconception. Data were collected using a three tier-test diagnostic test and analyzed descriptively quantitatively. The results showed that the level of misconception was in the two categories of high and medium levels. It needs an innovative teaching technique for subsequent research to treat Newton's Newton misconception.
Preconditioned Inexact Newton for Nonlinear Sparse Electromagnetic Imaging
Desmal, Abdulla
2014-05-04
Newton-type algorithms have been extensively studied in nonlinear microwave imaging due to their quadratic convergence rate and ability to recover images with high contrast values. In the past, Newton methods have been implemented in conjunction with smoothness promoting optimization/regularization schemes. However, this type of regularization schemes are known to perform poorly when applied in imagining domains with sparse content or sharp variations. In this work, an inexact Newton algorithm is formulated and implemented in conjunction with a linear sparse optimization scheme. A novel preconditioning technique is proposed to increase the convergence rate of the optimization problem. Numerical results demonstrate that the proposed framework produces sharper and more accurate images when applied in sparse/sparsified domains.
Preconditioned Inexact Newton for Nonlinear Sparse Electromagnetic Imaging
Desmal, Abdulla
2014-01-06
Newton-type algorithms have been extensively studied in nonlinear microwave imaging due to their quadratic convergence rate and ability to recover images with high contrast values. In the past, Newton methods have been implemented in conjunction with smoothness promoting optimization/regularization schemes. However, this type of regularization schemes are known to perform poorly when applied in imagining domains with sparse content or sharp variations. In this work, an inexact Newton algorithm is formulated and implemented in conjunction with a linear sparse optimization scheme. A novel preconditioning technique is proposed to increase the convergence rate of the optimization problem. Numerical results demonstrate that the proposed framework produces sharper and more accurate images when applied in sparse/sparsified domains.
Preconditioned Inexact Newton for Nonlinear Sparse Electromagnetic Imaging
Desmal, Abdulla; Bagci, Hakan
2014-01-01
Newton-type algorithms have been extensively studied in nonlinear microwave imaging due to their quadratic convergence rate and ability to recover images with high contrast values. In the past, Newton methods have been implemented in conjunction with smoothness promoting optimization/regularization schemes. However, this type of regularization schemes are known to perform poorly when applied in imagining domains with sparse content or sharp variations. In this work, an inexact Newton algorithm is formulated and implemented in conjunction with a linear sparse optimization scheme. A novel preconditioning technique is proposed to increase the convergence rate of the optimization problem. Numerical results demonstrate that the proposed framework produces sharper and more accurate images when applied in sparse/sparsified domains.
Investigation of vortex breakdown on a delta wing using Euler and Navier-Stokes equations
Agrawal, S.; Barnett, R. M.; Robinson, B. A.
1991-01-01
A numerical investigation of leading edge vortex breakdown in a delta wing at high angles of attack is presented. The analysis was restricted to low speed flows on a flat plate wing with sharp leading edges. Both Euler and Navier-Stokes equations were used and the results were compared with experimental data. Predictions of vortex breakdown progression with angle of attack with both Euler and Navier-Stokes equations are shown to be consistent with the experimental data. However, the Navier-Stokes predictions show significant improvements in breakdown location at angles of attack where the vortex breakdown approaches the wing apex. The predicted trajectories of the primary vortex are in very good agreement with the test data, the laminar solutions providing the overall best comparison. The Euler shows a small displacement of the primary vortex, relative to experiment, due to the lack of secondary vortices. The turbulent Navier-Stokes, in general, fall between the Euler and laminar solutions.
Analysis of the iteratively regularized Gauss-Newton method under a heuristic rule
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.
Scheunert, M.; Ullmann, A.; Afanasjew, M.; Börner, R.-U.; Siemon, B.; Spitzer, K.
2016-06-01
We present an inversion concept for helicopter-borne frequency-domain electromagnetic (HEM) data capable of reconstructing 3-D conductivity structures in the subsurface. Standard interpretation procedures often involve laterally constrained stitched 1-D inversion techniques to create pseudo-3-D models that are largely representative for smoothly varying conductivity distributions in the subsurface. Pronounced lateral conductivity changes may, however, produce significant artifacts that can lead to serious misinterpretation. Still, 3-D inversions of entire survey data sets are numerically very expensive. Our approach is therefore based on a cut-&-paste strategy whereupon the full 3-D inversion needs to be applied only to those parts of the survey where the 1-D inversion actually fails. The introduced 3-D Gauss-Newton inversion scheme exploits information given by a state-of-the-art (laterally constrained) 1-D inversion. For a typical HEM measurement, an explicit representation of the Jacobian matrix is inevitable which is caused by the unique transmitter-receiver relation. We introduce tensor quantities which facilitate the matrix assembly of the forward operator as well as the efficient calculation of the Jacobian. The finite difference forward operator incorporates the displacement currents because they may seriously affect the electromagnetic response at frequencies above 100. Finally, we deliver the proof of concept for the inversion using a synthetic data set with a noise level of up to 5%.
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.
Quasi-Newton methods for implicit black-box FSI coupling
CSIR Research Space (South Africa)
Bogaers, Alfred EJ
2014-09-01
Full Text Available In this paper we introduce a new multi-vector update quasi-Newton (MVQN) method for implicit coupling of partitioned, transient FSI solvers. The new quasi-Newton method facilitates the use of 'black-box' field solvers and under certain circumstances...
Dynamic Euler-Bernoulli Beam Equation: Classification and Reductions
Directory of Open Access Journals (Sweden)
R. Naz
2015-01-01
Full Text Available We study a dynamic fourth-order Euler-Bernoulli partial differential equation having a constant elastic modulus and area moment of inertia, a variable lineal mass density g(x, and the applied load denoted by f(u, a function of transverse displacement u(t,x. The complete Lie group classification is obtained for different forms of the variable lineal mass density g(x and applied load f(u. The equivalence transformations are constructed to simplify the determining equations for the symmetries. The principal algebra is one-dimensional and it extends to two- and three-dimensional algebras for an arbitrary applied load, general power-law, exponential, and log type of applied loads for different forms of g(x. For the linear applied load case, we obtain an infinite-dimensional Lie algebra. We recover the Lie symmetry classification results discussed in the literature when g(x is constant with variable applied load f(u. For the general power-law and exponential case the group invariant solutions are derived. The similarity transformations reduce the fourth-order partial differential equation to a fourth-order ordinary differential equation. For the power-law applied load case a compatible initial-boundary value problem for the clamped and free end beam cases is formulated. We deduce the fourth-order ordinary differential equation with appropriate initial and boundary conditions.
Directory of Open Access Journals (Sweden)
Fu Yuhua
2014-06-01
Full Text Available Neutrosophy is a new branch of philosophy, and "Quad-stage" (Four stages is the expansion of Hegel’s triad thesis, antithesis, synthesis of development. Applying Neutrosophy and "Quad-stage" method, the purposes of this paper are expanding Newton Mechanics and making it become New Newton Mechanics (NNW taking law of conservation of energy as unique source law. In this paper the examples show that in some cases other laws may be contradicted with the law of conservation of energy. The original Newton's three laws and the law of gravity, in principle can be derived by the law of conservation of energy. Through the example of free falling body, this paper derives the original Newton's second law by using the law of conservation of energy, and proves that there is not the contradiction between the original law of gravity and the law of conservation of energy; and through the example of a small ball rolls along the inclined plane (belonging to the problem cannot be solved by general relativity that a body is forced to move in flat space, derives improved Newton's second law and improved law of gravity by using law of conservation of energy. Whether or not other conservation laws (such as the law of conservation of momentum and the law of conservation of angular momentum can be utilized, should be tested by law of conservation of energy. When the original Newton's second law is not correct, then the laws of conservation of momentum and angular momentum are no longer correct; therefore the general forms of improved law of conservation of momentum and improved law of conservation of angular momentum are presented. In the cases that law of conservation of energy cannot be used effectively, New Newton Mechanics will not exclude that according to other theories or accurate experiments to derive the laws or formulas to solve some specific problems. For example, with the help of the result of general relativity, the improved Newton's formula of universal
Dynamic Newton-Puiseux Theorem
DEFF Research Database (Denmark)
Mannaa, Bassel; Coquand, Thierry
2013-01-01
A constructive version of Newton-Puiseux theorem for computing the Puiseux expansions of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization...
Newton\\'s equation of motion in the gravitational field of an oblate ...
African Journals Online (AJOL)
In this paper, we derived Newton's equation of motion for a satellite in the gravitational scalar field of a uniformly rotating, oblate spheriodal Earth using spheriodal coordinates. The resulting equation is solved for the corresponding precession and the result compared with similar ones. JONAMP Vol. 11 2007: pp. 279-286 ...
Measure-valued solutions to the complete Euler system revisited
Březina, Jan; Feireisl, Eduard
2018-06-01
We consider the complete Euler system describing the time evolution of a general inviscid compressible fluid. We introduce a new concept of measure-valued solution based on the total energy balance and entropy inequality for the physical entropy without any renormalization. This class of so-called dissipative measure-valued solutions is large enough to include the vanishing dissipation limits of the Navier-Stokes-Fourier system. Our main result states that any sequence of weak solutions to the Navier-Stokes-Fourier system with vanishing viscosity and heat conductivity coefficients generates a dissipative measure-valued solution of the Euler system under some physically grounded constitutive relations. Finally, we discuss the same asymptotic limit for the bi-velocity fluid model introduced by H.Brenner.
Weyl-Euler-Lagrange Equations of Motion on Flat Manifold
Directory of Open Access Journals (Sweden)
Zeki Kasap
2015-01-01
Full Text Available This paper deals with Weyl-Euler-Lagrange equations of motion on flat manifold. It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. Classical mechanics is one of the major subfields of mechanics. Also, one way of solving problems in classical mechanics occurs with the help of the Euler-Lagrange equations. In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. Additionally, the improvements, obtained in this study, will be presented.
Coupling of partitioned physics codes with quasi-Newton methods
CSIR Research Space (South Africa)
Haelterman, R
2017-03-01
Full Text Available , A class of methods for solving nonlinear simultaneous equations. Math. Comp. 19, pp. 577–593 (1965) [3] C.G. Broyden, Quasi-Newton methods and their applications to function minimization. Math. Comp. 21, pp. 368–381 (1967) [4] J.E. Dennis, J.J. More...´, Quasi-Newton methods: motivation and theory. SIAM Rev. 19, pp. 46–89 (1977) [5] J.E. Dennis, R.B. Schnabel, Least Change Secant Updates for quasi- Newton methods. SIAM Rev. 21, pp. 443–459 (1979) [6] G. Dhondt, CalculiX CrunchiX USER’S MANUAL Version 2...
Various Newton-type iterative methods for solving nonlinear equations
Directory of Open Access Journals (Sweden)
Manoj Kumar
2013-10-01
Full Text Available The aim of the present paper is to introduce and investigate new ninth and seventh order convergent Newton-type iterative methods for solving nonlinear equations. The ninth order convergent Newton-type iterative method is made derivative free to obtain seventh-order convergent Newton-type iterative method. These new with and without derivative methods have efficiency indices 1.5518 and 1.6266, respectively. The error equations are used to establish the order of convergence of these proposed iterative methods. Finally, various numerical comparisons are implemented by MATLAB to demonstrate the performance of the developed methods.
Problem in Two Unknowns: Robert Hooke and a Worm in Newton's Apple.
Weinstock, Robert
1992-01-01
Discusses the place that Robert Hooke has in science history versus the scientific contributions he made. Examines the relationship between Hooke and his contemporary, Isaac Newton, and Hooke's claims that Newton built on his ideas without receiving Newton's recognition. (26 references) (MDH)
Non-Relativistic Twistor Theory and Newton-Cartan Geometry
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.
DEFF Research Database (Denmark)
Strykowski, Gabriel; Larsen, Jacob Norby
2000-01-01
In this paper we advocate the use of Newton's law of gravitational attraction to ensure perfect consistency between gravity and height data. Starting with the absolute gravity on the topography we decompose this signal into a number of quantities associated with physics of the system. To model gr...
Was Newton right? A search for non-Newtonian behavior of weak-field gravity
Directory of Open Access Journals (Sweden)
Boynton Paul
2014-06-01
Full Text Available Empirical tests of Einstein’s metric theory of gravitation, even in the non-relativistic, weak-field limit, could play an important role in judging theory-driven extensions of the current Standard Model of fundamental interactions. Guided by Galileo's work and his own experiments, Newton formulated a theory of gravity in which the force of attraction between two bodies is independent of composition and proportional to the inertia of each, thereby transparently satisfying Galileo's empirically informed conjecture regarding the Universality of Free Fall. Similarly, Einstein honored the manifest success of Newton’s theory by assuring that the linearized equations of GTR matched the Newtonian formalism under “classical” conditions. Each of these steps, however, was explicitly an approximation raised to the status of principle. Perhaps, at some level, Newtonian gravity does not accurately describe the physical interaction between uncharged, unmagnetized, macroscopic bits of ordinary matter. What if Newton were wrong? Detecting any significant deviation from Newtonian behavior, no matter how small, could provide new insights and possibly reveal new physics. In the context of physics as an empirical science, for us this yet unanswered question constitutes sufficient motivation to attempt precision measurements of the kind described here. In this paper we report the current status of a project to search for violation of the Newtonian inverse square law of gravity.
On the classification of plane graphs representing structurally stable rational Newton flows
Jongen, H.Th.; Jonker, P.; Twilt, F.
1991-01-01
We study certain plane graphs, called Newton graphs, representing a special class of dynamical systems which are closely related to Newton's iteration method for finding zeros of (rational) functions defined on the complex plane. These Newton graphs are defined in terms of nonvanishing angles
Entropy viscosity method applied to Euler equations
International Nuclear Information System (INIS)
Delchini, M. O.; Ragusa, J. C.; Berry, R. A.
2013-01-01
The entropy viscosity method [4] has been successfully applied to hyperbolic systems of equations such as Burgers equation and Euler equations. The method consists in adding dissipative terms to the governing equations, where a viscosity coefficient modulates the amount of dissipation. The entropy viscosity method has been applied to the 1-D Euler equations with variable area using a continuous finite element discretization in the MOOSE framework and our results show that it has the ability to efficiently smooth out oscillations and accurately resolve shocks. Two equations of state are considered: Ideal Gas and Stiffened Gas Equations Of State. Results are provided for a second-order time implicit schemes (BDF2). Some typical Riemann problems are run with the entropy viscosity method to demonstrate some of its features. Then, a 1-D convergent-divergent nozzle is considered with open boundary conditions. The correct steady-state is reached for the liquid and gas phases with a time implicit scheme. The entropy viscosity method correctly behaves in every problem run. For each test problem, results are shown for both equations of state considered here. (authors)
Natural frequencies of Euler-Bernoulli beam with open cracks on elastic foundations
International Nuclear Information System (INIS)
Shin, Young Jae; Yun, Jong Hak; Seong, Kyeong Youn; Kim, Jae Ho; Kang, Sung Hwang
2006-01-01
A study of the natural vibrations of beam resting on elastic foundation with finite number of transverse open cracks is presented. Frequency equations are derived for beams with different end restraints. Euler-Bernoulli beam on Winkler foundation and Euler-Bernoulli beam on Paster nak foundation are investigated. The cracks are modeled by massless substitute spring. The effects of the crack location, size and its number and the foundation constants, on the natural frequencies of the beam, are investigated
A novel numerical flux for the 3D Euler equations with general equation of state
Toro, Eleuterio F.; Castro, Cristó bal E.; Bok Jik, Lee
2015-01-01
Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both
Phase reconstruction by a multilevel iteratively regularized Gauss–Newton method
International Nuclear Information System (INIS)
Langemann, Dirk; Tasche, Manfred
2008-01-01
In this paper we consider the numerical solution of a phase retrieval problem for a compactly supported, linear spline f : R → C with the Fourier transform f-circumflex, where values of |f| and |f-circumflex| at finitely many equispaced nodes are given. The unknown phases of complex spline coefficients fulfil a well-structured system of nonlinear equations. Thus the phase reconstruction leads to a nonlinear inverse problem, which is solved by a multilevel strategy and iterative Tikhonov regularization. The multilevel strategy concentrates the main effort of the solution of the phase retrieval problem in the coarse, less expensive levels and provides convenient initial guesses at the next finer level. On each level, the corresponding nonlinear system is solved by an iteratively regularized Gauss–Newton method. The multilevel strategy is motivated by convergence results of IRGN. This method is applicable to a wide range of examples as shown in several numerical tests for noiseless and noisy data
Conservative numerical schemes for Euler-Lagrange equations
Energy Technology Data Exchange (ETDEWEB)
Vazquez, L. [Universidad Complutense, Madrid (Spain). Dept. de Matematica Aplicada; Jimenez, S. [Universidad Alfonso X El Sabio, Madrid (Spain). Dept. de Matematica Aplicada
1999-05-01
As a preliminary step to study magnetic field lines, the authors seek numerical schemes that reproduce at discrete level the significant feature of the continuous model, based on an underling Lagrangian structure. The resulting scheme give discrete counterparts of the variation law for the energy as well of as the Euler-Lagrange equations and their symmetries.
Absolute calibration of the mass scale in the inverse problem of the physical theory of fireballs
Kalenichenko, V. V.
1992-08-01
A method of the absolute calibration of the mass scale is proposed for solving the inverse problem of the physical theory of fireballs. The method is based on data on the masses of fallen meteorites whose fireballs have been photographed in flight. The method can be applied to fireballs whose bodies have not experienced significant fragmentation during their flight in the atmosphere and have kept their shape relatively well. Data on the Lost City and Innisfree meteorites are used to calculate the calibration coefficients.
International Nuclear Information System (INIS)
Quigg, Chris
2007-01-01
In the classical physics we inherited from Isaac Newton, mass does not arise, it simply is. The mass of a classical object is the sum of the masses of its parts. Albert Einstein showed that the mass of a body is a measure of its energy content, inviting us to consider the origins of mass. The protons we accelerate at Fermilab are prime examples of Einsteinian matter: nearly all of their mass arises from stored energy. Missing mass led to the discovery of the noble gases, and a new form of missing mass leads us to the notion of dark matter. Starting with a brief guided tour of the meanings of mass, the colloquium will explore the multiple origins of mass. We will see how far we have come toward understanding mass, and survey the issues that guide our research today.
Eigenvalue Decomposition-Based Modified Newton Algorithm
Directory of Open Access Journals (Sweden)
Wen-jun Wang
2013-01-01
Full Text Available When the Hessian matrix is not positive, the Newton direction may not be the descending direction. A new method named eigenvalue decomposition-based modified Newton algorithm is presented, which first takes the eigenvalue decomposition of the Hessian matrix, then replaces the negative eigenvalues with their absolute values, and finally reconstructs the Hessian matrix and modifies the searching direction. The new searching direction is always the descending direction. The convergence of the algorithm is proven and the conclusion on convergence rate is presented qualitatively. Finally, a numerical experiment is given for comparing the convergence domains of the modified algorithm and the classical algorithm.
Newton da Costa and the school of Curitiba
Directory of Open Access Journals (Sweden)
Artibano Micali
2011-06-01
Full Text Available This paper intends to report on the beginning of the publications of Newton da Costa outside Brazil. Two mathematicians played an important role in this beginning: Marcel Guillaume from the University of Clermont-Ferrand and Paul Dedecker from the Universities of Lille and Liège. At the same time we recall the role played by Newton da Costa and Jayme Machado Cardoso in the development of what we call here the School of Curitiba [Escola de Curitiba]. Paraconsistent logic was initiated in this school under the influence of Newton da Costa. As another contribution of this school we mention the development of the theory of quasigroups; Jayme Machado Cardoso's name has been given, by Sade, to some particular objects which are now called Cardoso quasigroups.
International Nuclear Information System (INIS)
Cacciatori, Sergio L.; Cerchiai, Bianca L.; Della Vedova, Alberto; Ortenzi, Giovanni; Scotti, Antonio
2005-01-01
We provide a simple coordinatization for the group G 2 , which is analogous to the Euler coordinatization for SU(2). We show how to obtain the general element of the group in a form emphasizing the structure of the fibration of G 2 with fiber SO(4) and base H, the variety of quaternionic subalgebras of octonions. In particular this allows us to obtain a simple expression for the Haar measure on G 2 . Moreover, as a by-product it yields a concrete realization and an Einstein metric for H
Students’ misconceptions about Newton's second law in outer space
International Nuclear Information System (INIS)
Temiz, B K; Yavuz, A
2014-01-01
Students’ misconceptions about Newton's second law in frictionless outer space were investigated. The research was formed according to an epistemic game theoretical framework. The term ‘epistemic’ refers to students’ participation in problem-solving activities as a means of constructing new knowledge. The term ‘game’ refers to a coherent activity that consists of moves and rules. A set of questions in which students are asked to solve two similar Newton's second law problems, one of which is on the Earth and the other in outer space, was administered to 116 undergraduate students. The findings indicate that there is a significant difference between students’ epistemic game preferences and race-type (outer space or frictional surface) question. So students who used Newton's second law on the ground did not apply this law and used primitive reasoning when it came to space. Among these students, voluntary interviews were conducted with 18 students. Analysis of interview transcripts showed that: (1) the term ‘space’ causes spontaneity among students that prevents the use of the law; (2) students hesitate to apply Newton's second law in space due to the lack of a condition—the friction; (3) students feel that Newton's second law is not valid in space for a variety of reasons, but mostly for the fact that the body in space is not in contact with a surface. (paper)
The Adjoint Method for the Inverse Problem of Option Pricing
Directory of Open Access Journals (Sweden)
Shou-Lei Wang
2014-01-01
Full Text Available The estimation of implied volatility is a typical PDE inverse problem. In this paper, we propose the TV-L1 model for identifying the implied volatility. The optimal volatility function is found by minimizing the cost functional measuring the discrepancy. The gradient is computed via the adjoint method which provides us with an exact value of the gradient needed for the minimization procedure. We use the limited memory quasi-Newton algorithm (L-BFGS to find the optimal and numerical examples shows the effectiveness of the presented method.
Newton's Contributions to Optics
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 11; Issue 12. Newton's Contributions to Optics. Arvind Kumar. General Article Volume 11 Issue 12 December 2006 pp 10-20. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/011/12/0010-0020. Keywords.
Euler Strut: A Mechanical Analogy for Dynamics in the Vicinity of a Critical Point
Bobnar, Jaka; Susman, Katarina; Parsegian, V. Adrian; Rand, Peter R.; Cepic, Mojca; Podgornik, Rudolf
2011-01-01
An anchored elastic filament (Euler strut) under an external point load applied to its free end is a simple model for a second-order phase transition. In the static case, a load greater than the critical load causes a Euler buckling instability, leading to a change in the filament's shape. The analysis of filament dynamics with an external point…
Can Newton's Third Law Be "Derived" from the Second?
Gangopadhyaya, Asim; Harrington, James
2017-01-01
Newton's laws have engendered much discussion over several centuries. Today, the internet is awash with a plethora of information on this topic. We find many references to Newton's laws, often discussions of various types of misunderstandings and ways to explain them. Here we present an intriguing example that shows an assumption hidden in…
Zhang, Ling
2017-01-01
The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order [Formula: see text] to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.
Directory of Open Access Journals (Sweden)
Ling Zhang
2017-10-01
Full Text Available Abstract The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs. It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order 1 2 $\\frac{1}{2}$ to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.
A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise
Clason, Christian
2012-01-01
This work is concerned with nonlinear parameter identification in partial differential equations subject to impulsive noise. To cope with the non-Gaussian nature of the noise, we consider a model with L 1 fitting. However, the nonsmoothness of the problem makes its efficient numerical solution challenging. By approximating this problem using a family of smoothed functionals, a semismooth Newton method becomes applicable. In particular, its superlinear convergence is proved under a second-order condition. The convergence of the solution to the approximating problem as the smoothing parameter goes to zero is shown. A strategy for adaptively selecting the regularization parameter based on a balancing principle is suggested. The efficiency of the method is illustrated on several benchmark inverse problems of recovering coefficients in elliptic differential equations, for which one- and two-dimensional numerical examples are presented. © by SIAM.
Kohn's theorem, Larmor's equivalence principle and the Newton-Hooke group
International Nuclear Information System (INIS)
Gibbons, G.W.; Pope, C.N.
2011-01-01
Highlights: → We show that non-relativistic electrons moving in a magnetic field with trapping potential admits as relativity group the Newton-Hooke group. → We use this fact to give a group theoretic interpretation of Kohn's theorem and to obtain the spectrum. → We obtain the lightlike lift of the system exhibiting showing it coincides with the Nappi-Witten spacetime. - Abstract: We consider non-relativistic electrons, each of the same charge to mass ratio, moving in an external magnetic field with an interaction potential depending only on the mutual separations, possibly confined by a harmonic trapping potential. We show that the system admits a 'relativity group' which is a one-parameter family of deformations of the standard Galilei group to the Newton-Hooke group which is a Wigner-Inoenue contraction of the de Sitter group. This allows a group-theoretic interpretation of Kohn's theorem and related results. Larmor's theorem is used to show that the one-parameter family of deformations are all isomorphic. We study the 'Eisenhart' or 'lightlike' lift of the system, exhibiting it as a pp-wave. In the planar case, the Eisenhart lift is the Brdicka-Eardley-Nappi-Witten pp-wave solution of Einstein-Maxwell theory, which may also be regarded as a bi-invariant metric on the Cangemi-Jackiw group.
A variational principle for Newton-Cartan theory
International Nuclear Information System (INIS)
Goenner, H.F.M.
1984-01-01
In the framework of a space-time theory of gravitation a variational principle is set up for the gravitational field equations and the equations of motion of matter. The general framework leads to Newton's equations of motion with an unspecified force term and, for irrotational motion, to a restriction on the propagation of the shear tensor along the streamlines of matter. The field equations obtained from the variation are weaker than the standard field equations of Newton-Cartan theory. An application to fluids with shear and bulk viscosity is given. (author)
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.
Westfall, Richard S
1994-01-01
Le plus célèbre des savants, Isaac Newton, est aussi celui qui a le plus de biographes. Avant même sa mort, en 1727, l'un d'eux publiait un récit de la vie du grand homme. Richard Westfall, universitaire américain, est aujourd'hui le meilleur connaisseur d'un personnage en tout point extraordinaire, dont Aldous Huxley disait : « En tant qu'homme, c'est un fiasco ; en tant que monstre, il est superbe ! » Découvrant à 24 ans la loi de la gravitation universelle, établissant peu après les lois de l'optique tout en poursuivant des études alchimiques et théologiques, cet homme capable de rester des jours entiers sans manger ni dormir, absorbé par les énigmes du savoir, connaît une grave dépression dont il réchappe de justesse... pour se consacrer à l'économie de son pays : il devient directeur de la Monnaie de Londres, organisant une impitoyable chasse aux faux-monnayeurs ! L'image d'Épinal de Newton regardant une pomme tomber sort enrichie et complexifiée de ce livre fruit d'une vie de reche...
The Celestial Mechanics of Newton
Indian Academy of Sciences (India)
hannes Kepler had announced his first two laws of plan- etary motion (AD 1609), ... "Mathematical Principles of Natural Philosophy" .... He provided two different sets of proofs .... the Sun. Newton then formulated a theory of tides based on the.
Full waveform inversion for time-distance helioseismology
International Nuclear Information System (INIS)
Hanasoge, Shravan M.; Tromp, Jeroen
2014-01-01
Inferring interior properties of the Sun from photospheric measurements of the seismic wavefield constitutes the helioseismic inverse problem. Deviations in seismic measurements (such as wave travel times) from their fiducial values estimated for a given model of the solar interior imply that the model is inaccurate. Contemporary inversions in local helioseismology assume that properties of the solar interior are linearly related to measured travel-time deviations. It is widely known, however, that this assumption is invalid for sunspots and active regions and is likely for supergranular flows. Here, we introduce nonlinear optimization, executed iteratively, as a means of inverting for the subsurface structure of large-amplitude perturbations. Defining the penalty functional as the L 2 norm of wave travel-time deviations, we compute the total misfit gradient of this functional with respect to the relevant model parameters at each iteration around the corresponding model. The model is successively improved using either steepest descent, conjugate gradient, or the quasi-Newton limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Performing nonlinear iterations requires privileging pixels (such as those in the near field of the scatterer), a practice that is not compliant with the standard assumption of translational invariance. Measurements for these inversions, although similar in principle to those used in time-distance helioseismology, require some retooling. For the sake of simplicity in illustrating the method, we consider a two-dimensional inverse problem with only a sound-speed perturbation.
Inversion of convergent-beam electron diffraction patterns
International Nuclear Information System (INIS)
Bird, D.M.; Saunders, M.
1992-01-01
The problem of recovering the structure factors that contribute to a zone-axis convergent-beam diffraction pattern is discussed. It is shown that an automated matching procedure that minimizes the sum-of-squares difference between experimental and simulated patterns is effective whether one is refining accurate structure factors in a known crystal or attempting ab initio structure determination. The details of the minimization method are analysed and it is shown that a quasi-Newton method that uses analytically derived gradients is particulary effective when several structure factors are varied. The inversion method for ab initio structure determination is tested on the [110] axis of GaP, using simulated patterns as ideal 'experimental' data. (orig.)
Indian Academy of Sciences (India)
Home; Fellowship. Fellow Profile. Elected: 1935 Honorary. Lewis, Prof. Gilbert Newton. Date of birth: 25 October 1875. Date of death: 24 March 1946. YouTube; Twitter; Facebook; Blog. Academy News. IAS Logo. 29th Mid-year meeting. Posted on 19 January 2018. The 29th Mid-year meeting of the Academy will be held ...
Space and motion in nature and Scripture: Galileo, Descartes, Newton.
Janiak, Andrew
2015-06-01
In the Scholium to the Definitions in Principia mathematica, Newton departs from his main task of discussing space, time and motion by suddenly mentioning the proper method for interpreting Scripture. This is surprising, and it has long been ignored by scholars. In this paper, I argue that the Scripture passage in the Scholium is actually far from incidental: it reflects Newton's substantive concern, one evident in correspondence and manuscripts from the 1680s, that any general understanding of space, time and motion must enable readers to recognize the veracity of Biblical claims about natural phenomena, including the motion of the earth. This substantive concern sheds new light on an aspect of Newton's project in the Scholium. It also underscores Newton's originality in dealing with the famous problem of reconciling theological and philosophical conceptions of nature in the seventeenth century. Copyright © 2015 Elsevier Ltd. All rights reserved.
Parallel Implicit Algorithms for CFD
Keyes, David E.
1998-01-01
The main goal of this project was efficient distributed parallel and workstation cluster implementations of Newton-Krylov-Schwarz (NKS) solvers for implicit Computational Fluid Dynamics (CFD.) "Newton" refers to a quadratically convergent nonlinear iteration using gradient information based on the true residual, "Krylov" to an inner linear iteration that accesses the Jacobian matrix only through highly parallelizable sparse matrix-vector products, and "Schwarz" to a domain decomposition form of preconditioning the inner Krylov iterations with primarily neighbor-only exchange of data between the processors. Prior experience has established that Newton-Krylov methods are competitive solvers in the CFD context and that Krylov-Schwarz methods port well to distributed memory computers. The combination of the techniques into Newton-Krylov-Schwarz was implemented on 2D and 3D unstructured Euler codes on the parallel testbeds that used to be at LaRC and on several other parallel computers operated by other agencies or made available by the vendors. Early implementations were made directly in Massively Parallel Integration (MPI) with parallel solvers we adapted from legacy NASA codes and enhanced for full NKS functionality. Later implementations were made in the framework of the PETSC library from Argonne National Laboratory, which now includes pseudo-transient continuation Newton-Krylov-Schwarz solver capability (as a result of demands we made upon PETSC during our early porting experiences). A secondary project pursued with funding from this contract was parallel implicit solvers in acoustics, specifically in the Helmholtz formulation. A 2D acoustic inverse problem has been solved in parallel within the PETSC framework.
Water Rockets. Get Funny With Newton's Laws
Directory of Open Access Journals (Sweden)
Manuel Roca Vicent
2017-01-01
Full Text Available The study of the movement of the rocket has been used for decades to encourage students in the study of physics. This system has an undeniable interest to introduce concepts such as properties of gases, laws of Newton, exchange between different types of energy and its conservation or fluid mechanics. Our works has been to build and launch these rockets in different educational levels and in each of these ones have introduced the part of Physics more suited to the knowledge of our students. The aim of the learning experience is to launch the rocket as far as possible and learn to predict the travelled distance, using Newton's laws and fluid mechanics. After experimentation we demonstrated to be able to control the parameters that improve the performance of our rocket, such as the fill factor, the volume and mass of the empty bottle, liquid density, launch angle, pressure prior air release. In addition, it is a fun experience can be attached to all levels of education in primary and high school.
Astronomical and Cosmological Symbolism in Art Dedicated to Newton and Einstein
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.
Life after Newton: an ecological metaphysic.
Ulanowicz, R E
1999-05-01
Ecology may indeed be 'deep', as some have maintained, but perhaps much of the mystery surrounding it owes more simply to the dissonance between ecological notions and the fundamentals of the modern synthesis. Comparison of the axioms supporting the Newtonian world view with those underlying the organicist and stochastic metaphors that motivate much of ecosystems science reveals strong disagreements--especially regarding the nature of the causes of events and the scalar domains over which these causes can operate. The late Karl Popper held that the causal closure forced by our mechanical perspective on nature frustrates our attempts to achieve an 'evolutionary theory of knowledge.' He suggested that the Newtonian concept of 'force' must be generalized to encompass the contingencies that arise in evolutionary processes. His reformulation of force as 'propensity' leads quite naturally to a generalization of Newton's laws for ecology. The revised tenets appear, however, to exhibit more scope and allow for change to arise from within a system. Although Newton's laws survive (albeit in altered form) within a coalescing ecological metaphysic, the axioms that Enlightenment thinkers appended to Newton's work seem ill-suited for ecology and perhaps should yield to a new and coherent set of assumptions on how to view the processes of nature.
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)
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.
Catch a falling apple: Isaac Newton and myths of genius.
Fara, P
1999-01-01
Newton has become a legendary figure belonging to the distant past rather than a historical person who lived at a specific time. Historians and scientists have constantly reinterpreted many anecdotal tales describing Newton's achievements and behaviour, but the most famous concerns the falling apple in his country garden. Newton's apple conjures up multiple allegorical resonances, and examining its historical accuracy is less important than uncovering the mythical truths embedded within this symbol. Because interest groups fashion different collective versions of the past, analysing mythical tales can reveal fundamental yet conflicting attitudes towards science and its practices.
3-D cross-gradient joint inversion of seismic refraction and DC resistivity data
Shi, Zhanjie; Hobbs, Richard W.; Moorkamp, Max; Tian, Gang; Jiang, Lu
2017-06-01
We present a 3-D cross-gradient joint inversion algorithm for seismic refraction and DC resistivity data. The structural similarity between seismic slowness and resistivity models is enforced by a cross-gradient term in the objective function that also includes misfit and regularization terms. A limited memory quasi-Newton approach is used to perform the optimization of the objective function. To validate the proposed methodology and its implementation, tests were performed on a typical archaeological geophysical synthetic model. The results show that the inversion model and physical parameters estimated by our joint inversion method are more consistent with the true model than those from single inversion algorithm. Moreover, our approach appears to be more robust in conditions of noise. Finally, the 3-D cross-gradient joint inversion algorithm was applied to the field data from Lin_an ancient city site in Hangzhou of China. The 3-D cross-gradient joint inversion models are consistent with the archaeological excavation results of the ancient city wall remains. However, by single inversion, seismic slowness model does not show the anomaly of city wall remains and resistivity model does not fit well with the archaeological excavation results. Through these comparisons, we conclude that the proposed algorithm can be used to jointly invert 3-D seismic refraction and DC resistivity data to reduce the uncertainty brought by single inversion scheme.
ESA's XMM-Newton sees matter speed-racing around a black hole
2005-01-01
hi-res Size hi-res: 715 Kb Credits: NASA/Dana Berry, SkyWorks Digital ESA’s XMM-Newton sees matter speed-racing around a black hole Click here for animation in MOV format Movie still in TIFF format (9761 Kb) Movie still in JPG format (715 Kb) This animation depicts three hot chunks of matter orbiting a black hole. If placed in our Solar System, this black hole would appear like a dark abyss spread out nearly as wide as Mercury's orbit. And the three chunks (each as large as the Sun) would be as far out as Jupiter. They orbit the black hole in a lightning-quick 30 000 kilometres per second, over a tenth of the speed of light. hi-res Size hi-res: 220 Kb Credits: NASA/Dana Berry, SkyWorks Digital ESA’s XMM-Newton sees matter speed-racing around a black hole Click here for animation in MPG format Movie still in TIFF format (2553 Kb) Movie still in JPG format (220 Kb) This is a simplified illustration of two hot chunks of matter orbiting a black hole, showing how scientists tracked the blobs by observing their Doppler shift. First, we see one blob. Note how the energy emitted from this orbiting material rises to about 6.5 kilo-electron volt (an energy unit) as it moves towards us, and then falls to about 5.8 kilo-electron volt as it moves away. This is the 'Doppler effect' and a similar phenomenon happens with the changing pitch of a police siren. If it is approaching, the frequency of the sound is higher, but if it is receding the frequency is lower. Matter goes round and round; energy goes up and down. About 14 seconds into the animation, a second blob is added, which also displays a rise and fall in energy during its orbit. The observation, made with ESA’s XMM-Newton observatory, marks the first time scientists could trace individual blobs of shredded matter on a complete journey around a black hole. This provides a crucial measurement that has long been missing from black hole studies: an orbital period. Knowing this, scientists can measure black hole mass and
Has ESA's XMM-Newton cast doubt over dark energy?
2003-12-01
Galaxy cluster RXJ0847 hi-res Size hi-res: 100k Galaxy cluster RXJ0847 The fuzzy object at the centre of the frame is one of the galaxy clusters observed by XMM-Newton in its investigation of the distant Universe. The cluster, designated RXJ0847.2+3449, is about 7 000 million light years away, so we see it here as it was 7 000 million years ago, when the Universe was only about half of its present age. This cluster is made up of several dozen galaxies. Observations of eight distant clusters of galaxies, the furthest of which is around 10 thousand million light years away, were studied by an international group of astronomers led by David Lumb of ESA's Space Research and Technology Centre (ESTEC) in the Netherlands. They compared these clusters to those found in the nearby Universe. This study was conducted as part of the larger XMM-Newton Omega Project, which investigates the density of matter in the Universe under the lead of Jim Bartlett of the College de France. Clusters of galaxies are prodigious emitters of X-rays because they contain a large quantity of high-temperature gas. This gas surrounds galaxies in the same way as steam surrounds people in a sauna. By measuring the quantity and energy of X-rays from a cluster, astronomers can work out both the temperature of the cluster gas and also the mass of the cluster. Theoretically, in a Universe where the density of matter is high, clusters of galaxies would continue to grow with time and so, on average, should contain more mass now than in the past. Most astronomers believe that we live in a low-density Universe in which a mysterious substance known as 'dark energy' accounts for 70% of the content of the cosmos and, therefore, pervades everything. In this scenario, clusters of galaxies should stop growing early in the history of the Universe and look virtually indistinguishable from those of today. In a paper soon to be published by the European journal Astronomy and Astrophysics, astronomers from the XMM-Newton
Entropic corrections to Newton's law
International Nuclear Information System (INIS)
Setare, M R; Momeni, D; Myrzakulov, R
2012-01-01
In this short paper, we calculate separately the generalized uncertainty principle (GUP) and self-gravitational corrections to Newton's gravitational formula. We show that for a complete description of the GUP and self-gravity effects, both the temperature and entropy must be modified. (paper)
Newton's Principia: Myth and Reality
Smith, George
2016-03-01
Myths about Newton's Principia abound. Some of them, such as the myth that the whole book was initially developed using the calculus and then transformed into a geometric mathematics, stem from remarks he made during the priority controversy with Leibniz over the calculus. Some of the most persistent, and misleading, arose from failures to read the book with care. Among the latter are the myth that he devised his theory of gravity in order to explain the already established ``laws'' of Kepler, and that in doing so he took himself to be establishing that Keplerian motion is ``absolute,'' if not with respect to ``absolute space,'' then at least with respect to the fixed stars taken as what came later to be known as an inertial frame. The talk will replace these two myths with the reality of what Newton took himself to have established.
Newton Binomial Formulas in Schubert Calculus
Cordovez, Jorge; Gatto, Letterio; Santiago, Taise
2008-01-01
We prove Newton's binomial formulas for Schubert Calculus to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points.
Quantization effects on the inversion mode of a double gate MOS
Mondol, Kalyan; Hasan, Md. Manzurul; Arafath, Yeasir; Alam, Khairul
We investigate the quantization effects on the gate capacitance and charge distribution of a double gate MOSFET using a self-consistent solution of Poisson and Schrödinger equations of the industry standard simulation package Silvaco. Quantization effects on the gate C-V are simulated by varying the electron and hole effective masses. We notice that the inversion capacitance value decreases as the effective mass goes below 0.1mo and the shape of the C-V curve changes to step like in the inversion. We also notice that the inversion switches from surface inversion to volume inversion for low effective mass, and the quantization effect (step like shape) in C-V and volume inversion in charge profile happen at the same effective mass.
Ravat, Dhananjay
1996-01-01
The applicability of the Euler method of source location determination was investigated on several model situations pertinent to satellite-data scale situations as well as Magsat data of Europe. Our investigations enabled us to understand the end-member cases for which the Euler method will work with the present satellite magnetic data and also the cases for which the assumptions implicit in the Euler method will not be met by the present satellite magnetic data. These results have been presented in one invited lecture at the Indo-US workshop on Geomagnetism in Studies of the Earth's Interior in August 1994 in Pune, India, and at one presentation at the 21st General Assembly of the IUGG in July 1995 in Boulder, CO. A new method, called Anomaly Attenuation Rate (AAR) Method (based on the Euler method), was developed during this study. This method is scale-independent and is appropriate to locate centroids of semi-compact three dimensional sources of gravity and magnetic anomalies. The method was presented during 1996 Spring AGU meeting and a manuscript describing this method is being prepared for its submission to a high-ranking journal. The grant has resulted in 3 papers and presentations at national and international meetings and one manuscript of a paper (to be submitted shortly to a reputable journal).
International Nuclear Information System (INIS)
El-Nabulsi, Ahmad Rami
2009-01-01
Multidimensional fractional actionlike variational problem with time-dependent dynamical fractional exponents is constructed. Fractional Euler-Lagrange equations are derived and discussed in some details. The results obtained are used to explore some novel aspects of fractional quantum field theory where many interesting consequences are revealed, in particular the complexification of quantum field theory, in particular Dirac operators and the novel notion of 'mass without mass'.
An improved front tracking method for the Euler equations
Witteveen, J.A.S.; Koren, B.; Bakker, P.G.
2007-01-01
An improved front tracking method for hyperbolic conservation laws is presented. The improved method accurately resolves discontinuities as well as continuous phenomena. The method is based on an improved front interaction model for a physically more accurate modeling of the Euler equations, as
International Nuclear Information System (INIS)
Dias, Penha Maria Cardozo; Stuchi, T J
2013-01-01
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. (paper)
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.
Quantization effects on the inversion mode of a double gate MOS
Directory of Open Access Journals (Sweden)
Kalyan Mondol
Full Text Available We investigate the quantization effects on the gate capacitance and charge distribution of a double gate MOSFET using a self-consistent solution of Poisson and Schrödinger equations of the industry standard simulation package Silvaco. Quantization effects on the gate C–V are simulated by varying the electron and hole effective masses. We notice that the inversion capacitance value decreases as the effective mass goes below 0.1mo and the shape of the C–V curve changes to step like in the inversion. We also notice that the inversion switches from surface inversion to volume inversion for low effective mass, and the quantization effect (step like shape in C–V and volume inversion in charge profile happen at the same effective mass. Keywords: Double gate MOSFETs, Quantum effects, Energy quantization, Channel inversion, Charge density
VennDiagram: a package for the generation of highly-customizable Venn and Euler diagrams in R
Directory of Open Access Journals (Sweden)
Boutros Paul C
2011-01-01
Full Text Available Abstract Background Visualization of orthogonal (disjoint or overlapping datasets is a common task in bioinformatics. Few tools exist to automate the generation of extensively-customizable, high-resolution Venn and Euler diagrams in the R statistical environment. To fill this gap we introduce VennDiagram, an R package that enables the automated generation of highly-customizable, high-resolution Venn diagrams with up to four sets and Euler diagrams with up to three sets. Results The VennDiagram package offers the user the ability to customize essentially all aspects of the generated diagrams, including font sizes, label styles and locations, and the overall rotation of the diagram. We have implemented scaled Venn and Euler diagrams, which increase graphical accuracy and visual appeal. Diagrams are generated as high-definition TIFF files, simplifying the process of creating publication-quality figures and easing integration with established analysis pipelines. Conclusions The VennDiagram package allows the creation of high quality Venn and Euler diagrams in the R statistical environment.
VennDiagram: a package for the generation of highly-customizable Venn and Euler diagrams in R.
Chen, Hanbo; Boutros, Paul C
2011-01-26
Visualization of orthogonal (disjoint) or overlapping datasets is a common task in bioinformatics. Few tools exist to automate the generation of extensively-customizable, high-resolution Venn and Euler diagrams in the R statistical environment. To fill this gap we introduce VennDiagram, an R package that enables the automated generation of highly-customizable, high-resolution Venn diagrams with up to four sets and Euler diagrams with up to three sets. The VennDiagram package offers the user the ability to customize essentially all aspects of the generated diagrams, including font sizes, label styles and locations, and the overall rotation of the diagram. We have implemented scaled Venn and Euler diagrams, which increase graphical accuracy and visual appeal. Diagrams are generated as high-definition TIFF files, simplifying the process of creating publication-quality figures and easing integration with established analysis pipelines. The VennDiagram package allows the creation of high quality Venn and Euler diagrams in the R statistical environment.
A model reduction approach to numerical inversion for a parabolic partial differential equation
International Nuclear Information System (INIS)
Borcea, Liliana; Druskin, Vladimir; Zaslavsky, Mikhail; Mamonov, Alexander V
2014-01-01
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss–Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments. (paper)
A model reduction approach to numerical inversion for a parabolic partial differential equation
Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail
2014-12-01
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.
Canonical form of Euler-Lagrange equations and gauge symmetries
Energy Technology Data Exchange (ETDEWEB)
Geyer, B [Naturwissenschaftlich-Theoretisches Zentrum und Institut fuer Theoretische Physik, Universitaet Leipzig, Leipzig (Germany); Gitman, D M [Institute of Physics, University of Sao Paulo, Sao Paulo (Brazil); Tyutin, I V [Lebedev Physics Institute, Moscow (Russian Federation)
2003-06-13
The structure of the Euler-Lagrange equations for a general Lagrangian theory (e.g. singular, with higher derivatives) is studied. For these equations we present a reduction procedure to the so-called canonical form. In the canonical form the equations are solved with respect to highest-order derivatives of nongauge coordinates, whereas gauge coordinates and their derivatives enter the right-hand sides of the equations as arbitrary functions of time. The reduction procedure reveals constraints in the Lagrangian formulation of singular systems and, in that respect, is similar to the Dirac procedure in the Hamiltonian formulation. Moreover, the reduction procedure allows one to reveal the gauge identities between the Euler-Lagrange equations. Thus, a constructive way of finding all the gauge generators within the Lagrangian formulation is presented. At the same time, it is proved that for local theories all the gauge generators are local in time operators.
Three lectures on Newton's laws
Kokarev, Sergey S.
2009-01-01
Three small lectures are devoted to three Newton's laws, lying in the foundation of classical mechanics. These laws are analyzed from the viewpoint of our contemporary knowledge about space, time and physical interactions. The lectures were delivered for students of YarGU in RSEC "Logos".
XMM-Newton and Swift spectroscopy of the newly discovered very faint X-ray transient IGR J17494-3030
Armas Padilla, M.; Wijnands, R.; Degenaar, N.
2013-01-01
A growing group of low-mass X-ray binaries are found to be accreting at very faint X-ray luminosities of <1036 erg s−1 (2-10 keV). One such system is the new X-ray transient IGR J17494-3030. We present Swift and XMM-Newton observations obtained during its 2012 discovery outburst. The Swift
A primeira Lei de Newton: uma abordagem didática
da Silva, Saulo Luis Lima
2018-01-01
Resumo No estudo da mecânica Newtoniana o essencial é a compreensão das leis de Newton em profundidade. Se isso acontecer, ficará fácil perceber que todos os outros fenômenos a serem estudados são consequências dessas três leis básicas do movimento formuladas por Isaac Newton. Dentre elas, a primeira lei de Newton, conhecida como lei da Inércia, é a de maior complexidade filosófica e a menos compreendida pelos alunos ao saírem de um curso de física básica. Não é incomum encontrar alunos descr...
Newton law on the generalized singular brane with and without 4d induced gravity
International Nuclear Information System (INIS)
Jung, Eylee; Kim, Sung-Hoon; Park, D.K.
2003-01-01
Newton law arising due to the gravity localized on the general singular brane embedded in AdS 5 bulk is examined in the absence or presence of the 4d induced Einstein term. For the RS brane, apart from the subleading correction, Newton potential obeys 4d- and 5d-type gravitational law at long- and short-ranges if it were not for the induced Einstein term. The 4d induced Einstein term generates an intermediate range at short distance, in which the 5d Newton potential 1/r 2 emerges. For Neumann brane the long-range behavior of Newton potential is exponentially suppressed regardless of the existence of the induced Einstein term. For Dirichlet brane the expression of Newton potential is dependent on the renormalized coupling constant v ren . At particular value of v ren Newton potential on Dirichlet brane exhibits a similar behavior to that on RS brane. For other values the long-range behavior of Newton potential is exponentially suppressed as that in Neumann brane
Bryson, Dean Edward
of low-fidelity evaluations required. This narrowing of the search domain also alleviates the burden on the surrogate model corrections between the low- and high-fidelity data. Rather than requiring the surrogate to be accurate in a hyper-volume bounded by the trust region, the model needs only to be accurate along the forward-looking search direction. Maintaining the approximate inverse Hessian also allows the multifidelity algorithm to revert to high-fidelity optimization at any time. In contrast, the standard approach has no memory of the previously-computed high-fidelity data. The primary disadvantage of the proposed algorithm is that it may require modifications to the optimization software, whereas standard optimizers may be used as black-box drivers in the typical trust region method. A multifidelity, multidisciplinary simulation of aeroelastic vehicle performance is developed to demonstrate the optimization method. The numerical physics models include body-fitted Euler computational fluid dynamics; linear, panel aerodynamics; linear, finite-element computational structural mechanics; and reduced, modal structural bases. A central element of the multifidelity, multidisciplinary framework is a shared parametric, attributed geometric representation that ensures the analysis inputs are consistent between disciplines and fidelities. The attributed geometry also enables the transfer of data between disciplines. The new optimization algorithm, a standard trust region approach, and a single-fidelity quasi-Newton method are compared for a series of analytic test functions, using both polynomial chaos expansions and kriging to correct discrepancies between fidelity levels of data. In the aggregate, the new method requires fewer high-fidelity evaluations than the trust region approach in 51% of cases, and the same number of evaluations in 18%. The new approach also requires fewer low-fidelity evaluations, by up to an order of magnitude, in almost all cases. The efficacy
On the Local Type I Conditions for the 3D Euler Equations
Chae, Dongho; Wolf, Jörg
2018-05-01
We prove local non blow-up theorems for the 3D incompressible Euler equations under local Type I conditions. More specifically, for a classical solution {v\\in L^∞ (-1,0; L^2 ( B(x_0,r)))\\cap L^∞_{loc} (-1,0; W^{1, ∞} (B(x_0, r)))} of the 3D Euler equations, where {B(x_0,r)} is the ball with radius r and the center at x 0, if the limiting values of certain scale invariant quantities for a solution v(·, t) as {t\\to 0} are small enough, then { \
Symmetries of the Euler compressible flow equations for general equation of state
Energy Technology Data Exchange (ETDEWEB)
Boyd, Zachary M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ramsey, Scott D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Baty, Roy S. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-10-15
The Euler compressible flow equations exhibit different Lie symmetries depending on the equation of state (EOS) of the medium in which the flow occurs. This means that, in general, different types of similarity solution will be available in different flow media. We present a comprehensive classification of all EOS’s to which the Euler equations apply, based on the Lie symmetries admitted by the corresponding flow equations, restricting to the case of 1-D planar, cylindrical, or spherical geometry. The results are conveniently summarized in tables. This analysis also clarifies past work by Axford and Ovsiannikov on symmetry classification.
Browne, K. M.
2018-06-01
Ever since the beam balance was invented over three millennia ago, it has been used to measure what is now known as mass, but which, until the time of Newton, had always been known as "weight." Eugene Hecht recently discussed the concept of "mass" from medieval times to Newton's Principia, including the gradual change from philosophical to evidence based scientific thinking, but did not discuss the pre-Newtonian meaning of "weight" which then had the meaning of both weight and mass. The distinction between weight and mass was initiated by Kepler and completed by Newton.
Milgrom's revision of cosmic dynamics: Amending Newton's laws or Keplers
International Nuclear Information System (INIS)
Felten, J.E.
1983-12-01
Milgrom's recent revision of Newtonian dynamics was introduced to eliminate the inference that large quantities of invisible mass exist in galaxies. Simple examples show that a Milgrom acceleration, in the form presented so far, imply other far-reaching changes in dynamics. The momentum of an isolated system is not conserved, and the usual theorem for center-of-mass motion of any system does not hold. Naive applications require extreme caution. The model fails to provide a complete description of particle dynamics and should be thought of as a revision of Kepler's laws rather than Newton's. The Milgrom acceleration also implies fundamental changes in cosmology. A quasi-Newtonian calculation adapted from Newtonian cosmology suggests that a Milgrom universe will recollapse even if the classical closure parameter theta is less than 1. The solution, however, fails to satisfy the cosmological principle. Reasons for the breakdown of this calculation are examined. A theory of gravitation needed before the behavior of a Milgrom universe can be predicted
Milgrom's revision of cosmic dynamics: Amending Newton's laws or Keplers?
Felten, J. E.
1983-01-01
Milgrom's recent revision of Newtonian dynamics was introduced to eliminate the inference that large quantities of invisible mass exist in galaxies. Simple examples show that a Milgrom acceleration, in the form presented so far, imply other far-reaching changes in dynamics. The momentum of an isolated system is not conserved, and the usual theorem for center-of-mass motion of any system does not hold. Naive applications require extreme caution. The model fails to provide a complete description of particle dynamics and should be thought of as a revision of Kepler's laws rather than Newton's. The Milgrom acceleration also implies fundamental changes in cosmology. A quasi-Newtonian calculation adapted from Newtonian cosmology suggests that a Milgrom universe will recollapse even if the classical closure parameter theta is less than 1. The solution, however, fails to satisfy the cosmological principle. Reasons for the breakdown of this calculation are examined. A theory of gravitation needed before the behavior of a Milgrom universe can be predicted.
International Nuclear Information System (INIS)
Zhang, Haiwen; Zhang, Bo
2013-01-01
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves from a penetrable and a buried obstacle. By introducing a related transmission scattering problem, a Newton iteration method is proposed to simultaneously reconstruct both the penetrable interface and the buried obstacle inside from far-field data. The main feature of our method is that we do not need to know the type of boundary conditions on the buried obstacle. In particular, the boundary condition on the buried obstacle can also be determined simultaneously by the method. Finally, numerical examples using multi-frequency data are carried out to illustrate the effectiveness of our method. (paper)
XMM-Newton study of the supersoft symbiotic system Draco C1
Saeedi, Sara; Sasaki, Manami; Ducci, Lorenzo
2018-01-01
We present the results of the analysis of thirty-one XMM-Newton observations of the symbiotic star Draco C1 located in the Draco dwarf spheroidal galaxy. This object had been identified as a supersoft source based on ROSAT data. We analysed X-ray, ultraviolet (UV) and optical data taken with XMM-Newton in order to obtain the physical parameters and the geometry of the system. We have also performed the first X-ray timing analysis of Draco C1. The X-ray spectrum is well fitted with a blackbody model with a temperature of (1.8 ± 0.3) × 105 K. We obtained a bolometric luminosity of ≳1038 erg s-1 for the white dwarf. The X-ray spectrum and luminosity suggest stable nuclear burning on the surface of the white dwarf. The low column density derived from the X-ray spectrum is consistent with the lack of nebular lines found in previous UV studies. The long-term variability in the optical and the UV suggests that the system is not observed face-on and that the variability is caused by the reflection effect. For the red giant companion, we estimate a radius of ∼110 R⊙ and an upper limit ≲1.5 M⊙ for its mass assuming Roche lobe overflow.
XMM-Newton operations beyond the design lifetime
Parmar, Arvind N.; Kirsch, Marcus G. F.; Muñoz, J. Ramon; Santos-Lleo, Maria; Schartel, Norbert
2012-09-01
After more than twelve years in orbit and two years beyond the design lifetime, XMM-Newton continues its near faultless operations providing the worldwide astronomical community with an unprecedented combination of imaging and spectroscopic X-ray capabilities together with simultaneous optical and ultra-violet monitoring. The interest from the scientific community in observing with XMM-Newton remains extremely high with the last annual Announcement of Observing Opportunity (AO-11) attracting proposals requesting 6.7 times more observing time than was available. Following recovery from a communications problem in 2008, all elements of the mission are stable and largely trouble free. The operational lifetime if currently limited by the amount of available hydrazine fuel. XMM-Newton normally uses reaction wheels for attitude control and fuel is only used when offsetting reaction wheel speed away from limiting values and for emergency Sun acquisition following an anomaly. Currently, the hydrazine is predicted to last until around 2020. However, ESA is investigating the possibility of making changes to the operations concept and the onboard software that would enable lower fuel consumption. This could allow operations to well beyond 2026.
Zhou, Ting; Zeng, Jing; Liu, Shan; Zhao, Ting; Wu, Jie; Lai, Wenshi; He, Mingzhi; Xu, Beining; Qu, Shanshan; Xu, Ling; Tan, Wen
2015-10-01
The chiral inversion has been a concerned issue during the research and development of a chiral drug. In this study, a sensitive chiral liquid chromatography-tandem mass spectrometry (LC-MS/MS) method was developed for determination of salbutamol enantiomers in human plasma and urine. The chiral inversion mechanism of R-salbutamol was fully investigated for the first time by studying the effects of physicochemical factors, including pH, temperature and time. A fitted model to predict the chiral inversion ratio of R-salbutamol was proposed using a Box-Behnken design. All the samples were separated on an Astec Chirobiotic T column and detected by a tandem mass spectrometer in multiple reaction monitoring mode. Lower limit of quantification of 0.100ng/mL was achieved under the optimized conditions. The method was fully validated and successfully applied to the clinical pharmacokinetic study of R-salbutamol in healthy volunteers. Chiral inversion of R-salbutamol to S-salbutamol has been detected in urine samples. The results indicated that pH and temperature were two dominant factors that caused the chiral inversion of R-salbutamol, which should be taken into consideration during the analysis of chiral drugs. The chiral inversion of R-salbutamol determined in this study was confirmed resulted from the gastric acid in stomach rather than caused by the analysis conditions. Moreover, the calculated results of the fitted model matched very well with the enantioselective pharmacokinetic study of R-salbutamol, and the individual difference of the chiral inversion ratio of R-salbutamol was related to the individual gastric environment. On the basis of the results, this study provides important and concrete information not only for the chiral analysis but also for the metabolism research of chiral drugs. Copyright © 2015 Elsevier B.V. All rights reserved.
Newton's Telescope in Print: the Role of Images in the Reception of Newton's Instrument
Dupré, Sven
2008-01-01
While Newton tried to make his telescope into a proof of the supremacy of his theory of colours over older theories, his instrument was welcomed as a way to shorten telescopes, not as a way to solve the problem of chromatic aberration. This paper argues that the image published together with the
The frictional Schroedinger-Newton equation in models of wave function collapse
Energy Technology Data Exchange (ETDEWEB)
Diosi, Lajos [Research Institute for Particle and Nuclear Physics, H-1525 Budapest 114, PO Box 49 (Hungary)
2007-05-15
Replacing the Newtonian coupling G by -iG, the Schroedinger--Newton equation becomes {sup f}rictional{sup .} Instead of the reversible Schroedinger-Newton equation, we advocate its frictional version to generate the set of pointer states for macroscopic quantum bodies.
A preconditioned inexact newton method for nonlinear sparse electromagnetic imaging
Desmal, Abdulla
2015-03-01
A nonlinear inversion scheme for the electromagnetic microwave imaging of domains with sparse content is proposed. Scattering equations are constructed using a contrast-source (CS) formulation. The proposed method uses an inexact Newton (IN) scheme to tackle the nonlinearity of these equations. At every IN iteration, a system of equations, which involves the Frechet derivative (FD) matrix of the CS operator, is solved for the IN step. A sparsity constraint is enforced on the solution via thresholded Landweber iterations, and the convergence is significantly increased using a preconditioner that levels the FD matrix\\'s singular values associated with contrast and equivalent currents. To increase the accuracy, the weight of the regularization\\'s penalty term is reduced during the IN iterations consistently with the scheme\\'s quadratic convergence. At the end of each IN iteration, an additional thresholding, which removes small \\'ripples\\' that are produced by the IN step, is applied to maintain the solution\\'s sparsity. Numerical results demonstrate the applicability of the proposed method in recovering sparse and discontinuous dielectric profiles with high contrast values.
Multi-dimensional Fuzzy Euler Approximation
Directory of Open Access Journals (Sweden)
Yangyang Hao
2017-05-01
Full Text Available Multi-dimensional Fuzzy differential equations driven by multi-dimen-sional Liu process, have been intensively applied in many fields. However, we can not obtain the analytic solution of every multi-dimensional fuzzy differential equation. Then, it is necessary for us to discuss the numerical results in most situations. This paper focuses on the numerical method of multi-dimensional fuzzy differential equations. The multi-dimensional fuzzy Taylor expansion is given, based on this expansion, a numerical method which is designed for giving the solution of multi-dimensional fuzzy differential equation via multi-dimensional Euler method will be presented, and its local convergence also will be discussed.
Some aspects of the inverse problem of scattering at fixed energy
International Nuclear Information System (INIS)
Coudray, C.
1979-01-01
The first two chapters deal with the Newton-Sabatier method. Numerical tests are performed for real and complex potentials. They allow the study of the respective influences of energy, and of the internal parameters of the potential: its shape, depth and range. Within certain limits, good agreements are obtained. In particular, it is shown that they always require energies larger than a 'critical' energy, the dependence of which in function of the internal parameters of the potential being analyzed. Then the third chapter is devoted to transparent and quasi-transparent potentials in Born approximation. A class of such potentials is exhibited and studied. All of them oscillate, and their decrease at infinity may be chosen according to any arbitrary power of the variable. One of them is the Born approximation of the transparent potential of the Newton-Sabatier method. The last chapter concerns finite range complex potentials belonging to a well-defined class. For such potentials, a set of coherent inverse scattering date is given. The corresponding fundamental equation is written and shown to possess an unique solution [fr
Euler y la Conjetura de Fermat sobre Números Triangulares
Directory of Open Access Journals (Sweden)
José Manuel Sánchez Muñoz
2011-04-01
Full Text Available Este artículo describe la historia de como Euler demostró la existencia de infinitos números triangulares bicuadráticos, desde su correspondencia con su amigo Christian Goldbach hasta la publicación de sus resultados en la Academia de San Petesburgo.
Multipliers for the Absolute Euler Summability of Fourier Series
Indian Academy of Sciences (India)
In this paper, the author has investigated necessary and sufficient conditions for the absolute Euler summability of the Fourier series with multipliers. These conditions are weaker than those obtained earlier by some workers. It is further shown that the multipliers are best possible in certain sense.
Milgrom's revision of Newton's laws - Dynamical and cosmological consequences
Felten, J. E.
1984-01-01
Milgrom's (1983) recent revision of Newtonian dynamics was introduced to eliminate the inference that large quantities of invisible mass exist in galaxies. It is shown by simple examples that a Milgrom acceleration, in the form presented so far, implies other far-reaching changes in dynamics. The momentum of an isolated system is not conserved, and the usual theorem for center-of-mass motion of any system does not hold. Naive applications require extreme caution. The model fails to provide a complete description of particle dynamics and should be thought of as a revision of Kepler's laws rather than Newton's. The Milgrom acceleration also implies fundamental changes in cosmology. A quasi-Newtonian calculation adapted from Newtonian cosmology suggests that a 'Milgrom universe' will recollapse even if the classical closure parameter Omega is much less than unity. The solution, however, fails to satisfy the cosmological principle. Reasons for the breakdown of this calculation are examined. A new theory of gravitation will be needed before the behavior of a Milgrom universe can be predicted.
Uniqueness and numerical methods in inverse obstacle scattering
International Nuclear Information System (INIS)
Kress, Rainer
2007-01-01
The inverse problem we consider in this tutorial is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the first part we will concentrate on the issue of uniqueness, i.e., we will investigate under what conditions an obstacle and its boundary condition can be identified from a knowledge of its far field pattern for incident plane waves. We will review some classical and some recent results and draw attention to open problems. In the second part we will survey on numerical methods for solving inverse obstacle scattering problems. Roughly speaking, these methods can be classified into three groups. Iterative methods interpret the inverse obstacle scattering problem as a nonlinear ill-posed operator equation and apply iterative schemes such as regularized Newton methods, Landweber iterations or conjugate gradient methods for its solution. Decomposition methods, in principle, separate the inverse scattering problem into an ill-posed linear problem to reconstruct the scattered wave from its far field and the subsequent determination of the boundary of the scatterer from the boundary condition. Finally, the third group consists of the more recently developed sampling methods. These are based on the numerical evaluation of criteria in terms of indicator functions that decide whether a point lies inside or outside the scatterer. The tutorial will give a survey by describing one or two representatives of each group including a discussion on the various advantages and disadvantages
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
Frequency-domain full-waveform inversion with non-linear descent directions
Geng, Yu; Pan, Wenyong; Innanen, Kristopher A.
2018-05-01
Full-waveform inversion (FWI) is a highly non-linear inverse problem, normally solved iteratively, with each iteration involving an update constructed through linear operations on the residuals. Incorporating a flexible degree of non-linearity within each update may have important consequences for convergence rates, determination of low model wavenumbers and discrimination of parameters. We examine one approach for doing so, wherein higher order scattering terms are included within the sensitivity kernel during the construction of the descent direction, adjusting it away from that of the standard Gauss-Newton approach. These scattering terms are naturally admitted when we construct the sensitivity kernel by varying not the current but the to-be-updated model at each iteration. Linear and/or non-linear inverse scattering methodologies allow these additional sensitivity contributions to be computed from the current data residuals within any given update. We show that in the presence of pre-critical reflection data, the error in a second-order non-linear update to a background of s0 is, in our scheme, proportional to at most (Δs/s0)3 in the actual parameter jump Δs causing the reflection. In contrast, the error in a standard Gauss-Newton FWI update is proportional to (Δs/s0)2. For numerical implementation of more complex cases, we introduce a non-linear frequency-domain scheme, with an inner and an outer loop. A perturbation is determined from the data residuals within the inner loop, and a descent direction based on the resulting non-linear sensitivity kernel is computed in the outer loop. We examine the response of this non-linear FWI using acoustic single-parameter synthetics derived from the Marmousi model. The inverted results vary depending on data frequency ranges and initial models, but we conclude that the non-linear FWI has the capability to generate high-resolution model estimates in both shallow and deep regions, and to converge rapidly, relative to a
DEFF Research Database (Denmark)
Simonsen, Maria; Schiøler, Henrik; Leth, John-Josef
2014-01-01
The Euler-Maruyama method is applied to a simple stochastic differential equation (SDE) with discontinuous drift. Convergence aspects are investigated in the case, where the Euler-Maruyama method is simulated in dyadic points. A strong rate of convergence is presented for the numerical simulations...
Newton's Path to Universal Gravitation: The Role of the Pendulum
Boulos, Pierre J.
2006-01-01
Much attention has been given to Newton's argument for Universal Gravitation in Book III of the "Principia". Newton brings an impressive array of phenomena, along with the three laws of motion, and his rules for reasoning to deduce Universal Gravitation. At the centre of this argument is the famous "moon test". Here it is the empirical evidence…
Disk-galaxy density distribution from orbital speeds using Newton's law
Nicholson, Kenneth F.
2000-01-01
Given the dimensions (including thickness) of an axisymmetric galaxy, Newton's law is used in integral form to find the density distributions required to match a wide range of orbital speed profiles. Newton's law is not modified and no dark matter halos are required. The speed distributiions can have extreme shapes if they are reasonably smooth. Several examples are given.
N=2 superconformal Newton-Hooke algebra and many-body mechanics
International Nuclear Information System (INIS)
Galajinsky, Anton
2009-01-01
A representation of the conformal Newton-Hooke algebra on a phase space of n particles in arbitrary dimension which interact with one another via a generic conformal potential and experience a universal cosmological repulsion or attraction is constructed. The minimal N=2 superconformal extension of the Newton-Hooke algebra and its dynamical realization in many-body mechanics are studied.
On the Shoulders of Sir Isaac Newton and Arthur Storer
Martin, Helen E.; Evans-Gondo, Bonita
2013-01-01
Helen E. Martin, the author of this article, is a retired National Board Certified Teacher who has been researching Sir Isaac Newton's unpublished manuscripts for over three decades. While researching the work of Newton, a teacher she was mentoring asked for some hands-on activities to study planetary motion. The description of the activity…
International Nuclear Information System (INIS)
Kaltenbacher, Barbara; Kirchner, Alana; Vexler, Boris
2011-01-01
Parameter identification problems for partial differential equations usually lead to nonlinear inverse problems. A typical property of such problems is their instability, which requires regularization techniques, like, e.g., Tikhonov regularization. The main focus of this paper will be on efficient methods for determining a suitable regularization parameter by using adaptive finite element discretizations based on goal-oriented error estimators. A well-established method for the determination of a regularization parameter is the discrepancy principle where the residual norm, considered as a function i of the regularization parameter, should equal an appropriate multiple of the noise level. We suggest to solve the resulting scalar nonlinear equation by an inexact Newton method, where in each iteration step, a regularized problem is solved at a different discretization level. The proposed algorithm is an extension of the method suggested in Griesbaum A et al (2008 Inverse Problems 24 025025) for linear inverse problems, where goal-oriented error estimators for i and its derivative are used for adaptive refinement strategies in order to keep the discretization level as coarse as possible to save computational effort but fine enough to guarantee global convergence of the inexact Newton method. This concept leads to a highly efficient method for determining the Tikhonov regularization parameter for nonlinear ill-posed problems. Moreover, we prove that with the so-obtained regularization parameter and an also adaptively discretized Tikhonov minimizer, usual convergence and regularization results from the continuous setting can be recovered. As a matter of fact, it is shown that it suffices to use stationary points of the Tikhonov functional. The efficiency of the proposed method is demonstrated by means of numerical experiments. (paper)
Brauer, Uwe; Karp, Lavi
2018-01-01
Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density ρ which either falls off at infinity or has compact support. The solutions have finite mass, finite energy functional and include the static spherical solutions for γ = 6/5. The result is achieved by using weighted Sobolev spaces of fractional order and a new non-linear estimate which allows to estimate the physical density by the regularised non-linear matter variable. Gamblin also has studied this setting but using very different functional spaces. However we believe that the functional setting we use is more appropriate to describe a physical isolated body and more suitable to study the Newtonian limit.
Laboratory Test of Newton's Second Law for Small Accelerations
International Nuclear Information System (INIS)
Gundlach, J. H.; Schlamminger, S.; Spitzer, C. D.; Choi, K.-Y.; Woodahl, B. A.; Coy, J. J.; Fischbach, E.
2007-01-01
We have tested the proportionality of force and acceleration in Newton's second law, F=ma, in the limit of small forces and accelerations. Our tests reach well below the acceleration scales relevant to understanding several current astrophysical puzzles such as the flatness of galactic rotation curves, the Pioneer anomaly, and the Hubble acceleration. We find good agreement with Newton's second law at accelerations as small as 5x10 -14 m/s 2
DEFF Research Database (Denmark)
Cai, Hongzhu; Zhdanov, Michael
2015-01-01
to be discretized for the calculation of gravity field. This was especially significant in the modeling and inversion of gravity data for determining the depth to the basement. Another important result was developing a novel method of inversion of gravity data to recover the depth to basement, based on the 3D...... Cauchy-type integral representation. Our numerical studies determined that the new method is much faster than conventional volume discretization method to compute the gravity response. Our synthetic model studies also showed that the developed inversion algorithm based on Cauchy-type integral is capable......One of the most important applications of gravity surveys in regional geophysical studies is determining the depth to basement. Conventional methods of solving this problem are based on the spectrum and/or Euler deconvolution analysis of the gravity field and on parameterization of the earth...
Contact discontinuities in multi-dimensional isentropic Euler equations
Czech Academy of Sciences Publication Activity Database
Březina, J.; Chiodaroli, E.; Kreml, Ondřej
2018-01-01
Roč. 2018 (2018), č. článku 94. ISSN 1072-6691 R&D Projects: GA ČR(CZ) GJ17-01694Y Institutional support: RVO:67985840 Keywords : isentropic Euler equations * non-uniqueness * Riemann problem Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.954, year: 2016 https://ejde.math.txstate.edu/Volumes/2018/94/abstr.html
Formulation matricielle des equations du mouvement d'un solide ...
African Journals Online (AJOL)
Plusieurs formulations des équations du mouvement d'un rigide ont été développées. Le bien connu d'entre elles est celle de Newton-Euler; elle est généralement appelée «équations d'Euler classiques". Cette formulation donne six équations scalaires pour un corps rigide. Dans cet article, nous avons décrit les équations ...
A general multiblock Euler code for propulsion integration. Volume 1: Theory document
Chen, H. C.; Su, T. Y.; Kao, T. J.
1991-01-01
A general multiblock Euler solver was developed for the analysis of flow fields over geometrically complex configurations either in free air or in a wind tunnel. In this approach, the external space around a complex configuration was divided into a number of topologically simple blocks, so that surface-fitted grids and an efficient flow solution algorithm could be easily applied in each block. The computational grid in each block is generated using a combination of algebraic and elliptic methods. A grid generation/flow solver interface program was developed to facilitate the establishment of block-to-block relations and the boundary conditions for each block. The flow solver utilizes a finite volume formulation and an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. The generality of the method was demonstrated through the analysis of two complex configurations at various flow conditions. Results were compared to available test data. Two accompanying volumes, user manuals for the preparation of multi-block grids (vol. 2) and for the Euler flow solver (vol. 3), provide information on input data format and program execution.
Energy Technology Data Exchange (ETDEWEB)
Schubert, Sven
2008-09-15
The attempt to explain the rotational curves of spiral galaxies by means of Newton's gravitational law fails. There, where gravitational accelerations a{sub G}<10{sup -10} m/s{sup 2} act, the prediction no more agrees with the observation. Two alternatives are discussed: Either in the galaxies dark matter exists, wehich is just so distributed that the dynamics in the galaxies change as wanted. Ore the gravitational law must be corrected in the limit of small accelerations. This approach is called MOND (Modified Newtonian Dynamic). In this thesis an experiment is presented, which allows to check Newton's gravitational law at small values of the acceleration: Two spherical reflectors pend oppositely in a distance of 24 cm on tungsten wires and form a microwave resonator. On both sides of the resonator a test mass with a weight between 2.9 and 20.1 kg is located. If these masses are moved to and fro, their gravitational force effects a distance change {delta}b of the mirrors by around 0.3 to 20.0 nm. This can be determined via the shift of the resonance frequency of the resonator accurately determined up to 10{sup 12}m. Because of the low weight of the test masses on the mirrors accelerations a{sub G}{approx}10{sup 10} m/s{sup 2} act. If the measurement is performed with different, at left anf right however identical masses M, {delta}b{proportional_to}M should result, if Newton's gravitational laws is valid in the limit of small accelerations. In this thesis the controls necessary for the measurement and the calculator driving are described. Finally the results of a first resonance measurement are presented.
Iterative and range test methods for an inverse source problem for acoustic waves
International Nuclear Information System (INIS)
Alves, Carlos; Kress, Rainer; Serranho, Pedro
2009-01-01
We propose two methods for solving an inverse source problem for time-harmonic acoustic waves. Based on the reciprocity gap principle a nonlinear equation is presented for the locations and intensities of the point sources that can be solved via Newton iterations. To provide an initial guess for this iteration we suggest a range test algorithm for approximating the source locations. We give a mathematical foundation for the range test and exhibit its feasibility in connection with the iteration method by some numerical examples
Polarization of electron-positron vacuum by strong magnetic field in theory with fundamental mass
International Nuclear Information System (INIS)
Kadyshevskij, V.G.; ); Rodionov, V.N.
2003-01-01
The exact Lagrangian function of the intensive constant magnetic field, replacing the Heisenberg-Euler Lagrangian in the traditional quantum electrodynamics, is calculated within the frames of the theory with the fundamental mass in the single-loop approximation. It is established that the obtained generalization of the Lagrangian function is substantial by arbitrary values of the magnetic field. The calculated Lagrangian in the weak field coincides with the known Heisenberg-Euler formula. The Lagrangian dependence on the field in the extremely strong fields completely disappears and it tends in this area to the threshold value, which is determined by the fundamental and lepton mass ratio [ru
Precision Mass Measurements of Cr-6358 : Nuclear Collectivity Towards the N =40 Island of Inversion
Mougeot, M.; Atanasov, D.; Blaum, K.; Chrysalidis, K.; Goodacre, T. Day; Fedorov, D.; Fedosseev, V.; George, S.; Herfurth, F.; Holt, J. D.; Lunney, D.; Manea, V.; Marsh, B.; Neidherr, D.; Rosenbusch, M.; Rothe, S.; Schweikhard, L.; Schwenk, A.; Seiffert, C.; Simonis, J.; Stroberg, S. R.; Welker, A.; Wienholtz, F.; Wolf, R. N.; Zuber, K.
2018-06-01
The neutron-rich isotopes Cr 58 - 63 were produced for the first time at the ISOLDE facility and their masses were measured with the ISOLTRAP spectrometer. The new values are up to 300 times more precise than those in the literature and indicate significantly different nuclear structure from the new mass-surface trend. A gradual onset of deformation is found in this proton and neutron midshell region, which is a gateway to the second island of inversion around N =40 . In addition to comparisons with density-functional theory and large-scale shell-model calculations, we present predictions from the valence-space formulation of the ab initio in-medium similarity renormalization group, the first such results for open-shell chromium isotopes.
Judaism in the theology of Sir Isaac Newton
Goldish, Matt
1998-01-01
This book is based on my doctoral dissertation from the Hebrew University of Jerusalem (1996) of the same title. As a master's student, working on an entirely different project, I was well aware that many of Newton's theological manuscripts were located in our own Jewish National and University Library, but I was under the mistaken assumption that scores of highly qualified scholars must be assiduously scouring them and publishing their results. It never occurred to me to look at them at all until, having fmished my master's, I spoke to Professor David Katz at Tel-Aviv University about an idea I had for doctoral research. Professor Katz informed me that the project I had suggested was one which he himself had just fmished, but that I might be interested in working on the famous Newton manuscripts in the context of a project being organized by him, Richard Popkin, James Force, and the late Betty Jo Teeter Dobbs, to study and publish Newton's theological material. I asked him whether he was not sending me into ...
A domain derivative-based method for solving elastodynamic inverse obstacle scattering problems
International Nuclear Information System (INIS)
Le Louër, Frédérique
2015-01-01
The present work is concerned with the shape reconstruction problem of isotropic elastic inclusions from far-field data obtained by the scattering of a finite number of time-harmonic incident plane waves. This paper aims at completing the theoretical framework which is necessary for the application of geometric optimization tools to the inverse transmission problem in elastodynamics. The forward problem is reduced to systems of boundary integral equations following the direct and indirect methods initially developed for solving acoustic transmission problems. We establish the Fréchet differentiability of the boundary to far-field operator and give a characterization of the first Fréchet derivative and its adjoint operator. Using these results we propose an inverse scattering algorithm based on the iteratively regularized Gauß–Newton method and show numerical experiments in the special case of star-shaped obstacles. (paper)
Dynamic behaviour of non-uniform Bernoulli-Euler beams subjected ...
African Journals Online (AJOL)
This paper investigates the dynamics behaviour of non-uniform Bernoulli-Euler beams subjected to concentrated loads ravelling at variable velocities. The solution technique is based on the Generalized Galerkin Method and the use of the generating function of the Bessel function type. The results show that, for all the ...
International Nuclear Information System (INIS)
Kılıç, Emre; Eibert, Thomas F.
2015-01-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained
Energy Technology Data Exchange (ETDEWEB)
Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.
2015-05-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.
What are the Hidden Quantum Processes Behind Newton's Laws?
Ostoma, Tom; Trushyk, Mike
1999-01-01
We investigate the hidden quantum processes that are responsible for Newton's laws of motion and Newton's universal law of gravity. We apply Electro-Magnetic Quantum Gravity or EMQG to investigate Newtonian classical physics. EQMG is a quantum gravity theory that is manifestly compatible with Cellular Automata (CA) theory, a new paradigm for physical reality. EMQG is also based on a theory of inertia proposed by R. Haisch, A. Rueda, and H. Puthoff, which we modified and called Quantum Inertia...
Modeling the Motion of an Increasing Mass System
Kunkel, William; Harrington, Randal
2010-01-01
Problems on the dynamics of changing mass systems often call for the more general form of Newton's second law Fnet = dp/dt. These problems usually involve situations where the mass of the system decreases, such as in rocket propulsion. In contrast, this experiment examines a system where the mass "increases" at a constant rate and the net force…
Directory of Open Access Journals (Sweden)
Feifei Wang
Full Text Available BACKGROUND: Recent studies have revealed that body mass index (BMI inversely influenced serum glycated albumin (GA, which may cause an underestimation of GA-monitored short-term hyperglycemic control. OBJECTIVE: This study was to investigate the association between anthropometric variables (BMI and waist circumference (W and accurate adiposity variables (percentage of body fat (%fat, fat mass, free fat mass (FFM, subcutaneous fat area (SFA, and visceral fat area (VFA with serum GA. DESIGN: A total of 2563 subjects (1037 men, 593 premenopausal women, and 933 postmenopausal women with normal glucose tolerance underwent bioelectrical impedance body fat content measurement and magnetic resonance imaging. Serum GA and absolute value of GA (aGA were measured by enzymatic assay. RESULTS: Compared to the BMI <25.0 kg/m(2 group, the BMI ≥25.0 kg/m(2 group had significantly higher fasting plasma glucose, glycated hemoglobin A1c, and body fat parameters including W, %fat, fat mass, FFM, SFA, and VFA, but significantly lower aGA, and GA in all the three sex- and menopause-stratified groups (all P<0.05. GA decreased with the increment of fat mass for all three groups (all P for trend <0.001. In the same BMI category, men and postmenopausal women with elevated %fat (men, ≥25%; women, ≥35% still had significantly lower GA than those with normal %fat (men, <25%; women, <35% (all P<0.05. Multiple stepwise regression showed that %fat, fat mass, and VFA were independently associated with GA. CONCLUSIONS: Serum GA was inversely influenced by fat mass and visceral adipose tissue in Chinese with normal glucose tolerance.
The symplectic structure of Euler-Lagrange superequations and Batalin-Vilkoviski formalism
Monterde, J
2003-01-01
We study the graded Euler-Lagrange equations from the viewpoint of graded Poincare-Cartan forms. An application to a certain class of solutions of the Batalin-Vilkoviski master equation is also given.
Discovery Science: Newton All around You.
Prigo, Robert; Humphrey, Gregg
1993-01-01
Presents activities for helping elementary students learn about Newton's third law of motion. Several activity cards demonstrate the concept of the law of action and reaction. The activities require only inexpensive materials that can be found around the house. (SM)
Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbance
Directory of Open Access Journals (Sweden)
Pengcheng HAN
2017-12-01
Full Text Available In order to enrich the system stability theory of the control theories, taking Euler-Bernoulli beam equation as the research subject, the stability of Euler-Bernoulli beam equation with locally distributed disturbance is studied. A feedback controller based on output is designed to reduce the effects of the disturbances. The well-posedness of the nonlinear closed-loop system is investigated by the theory of maximal monotone operator, namely the existence and uniqueness of solutions for the closed-loop system. An appropriate state space is established, an appropriate inner product is defined, and a non-linear operator satisfying this state space is defined. Then, the system is transformed into the form of evolution equation. Based on this, the existence and uniqueness of solutions for the closed-loop system are proved. The asymptotic stability of the system is studied by constructing an appropriate Lyapunov function, which proves the asymptotic stability of the closed-loop system. The result shows that designing proper anti-interference controller is the foundation of investigating the system stability, and the research of the stability of Euler-bernoulli beam equation with locally distributed disturbance can prove the asymptotic stability of the system. This method can be extended to study the other equations such as wave equation, Timoshenko beam equation, Schrodinger equation, etc.
Wing aeroelasticity analysis based on an integral boundary-layer method coupled with Euler solver
Directory of Open Access Journals (Sweden)
Ma Yanfeng
2016-10-01
Full Text Available An interactive boundary-layer method, which solves the unsteady flow, is developed for aeroelastic computation in the time domain. The coupled method combines the Euler solver with the integral boundary-layer solver (Euler/BL in a “semi-inverse” manner to compute flows with the inviscid and viscous interaction. Unsteady boundary conditions on moving surfaces are taken into account by utilizing the approximate small-perturbation method without moving the computational grids. The steady and unsteady flow calculations for the LANN wing are presented. The wing tip displacement of high Reynolds number aero-structural dynamics (HIRENASD Project is simulated under different angles of attack. The flutter-boundary predictions for the AGARD 445.6 wing are provided. The results of the interactive boundary-layer method are compared with those of the Euler method and experimental data. The study shows that viscous effects are significant for these cases and the further data analysis confirms the validity and practicability of the coupled method.
Fundamentos kantianos dos axiomas do movimento de Newton
Vieira Coutinho Abreu Gomes, Írio
2006-01-01
Esse trabalho se insere na perspectiva fundacionista kantiana, particularmente no que diz respeito às três leis de Newton. Em sua obra de 1786, Princípios Metafísicos da Ciência da Natureza, Kant empreende a tarefa de fundamentar a física mecânica através de princípios metafísicos. Nosso objetivo nessa dissertação foi abordar essa obra especificamente em seu terceiro capítulo onde Kant trata dos axiomas do movimento de Newton. Nessa dissertação elucidamos a argumentação kantiana na fundamenta...
Newton's Law of Cooling Revisited
Vollmer, M.
2009-01-01
The cooling of objects is often described by a law, attributed to Newton, which states that the temperature difference of a cooling body with respect to the surroundings decreases exponentially with time. Such behaviour has been observed for many laboratory experiments, which led to a wide acceptance of this approach. However, the heat transfer…
Generalized force in classical field theory. [Euler-Lagrange equations
Energy Technology Data Exchange (ETDEWEB)
Krause, J [Universidad Central de Venezuela, Caracas
1976-02-01
The source strengths of the Euler-Lagrange equations, for a system of interacting fields, are heuristically interpreted as generalized forces. The canonical form of the energy-momentum tensor thus consistently appears, without recourse to space-time symmetry arguments. A concept of 'conservative' generalized force in classical field theory is also briefly discussed.
A Short Proof of Euler's Inequality R ≥ 2r Theorem. Let ∆ ABC be an ...
Indian Academy of Sciences (India)
IAS Admin
A Short Proof of Euler's Inequality R ≥ 2r. Theorem. Let ∆ ABC be an arbitrary triangle with circumradius R and inradius r. Then R ≥ 2r with equality holding if and only if ∆ABC is equilateral. This was first published by Euler in 1765. Since then several proofs have followed, some geometric and some algebraic. We will use ...
On-the-fly XMM-Newton Spacecraft Data Reduction on the Grid
Directory of Open Access Journals (Sweden)
A. Ibarra
2006-01-01
Full Text Available We present the results of the first prototype of a XMM-Newton pipeline processing task, parallelized at a CCD level, which can be run in a Grid system. By using the Grid Way application and the XMM-Newton Science Archive system, the processing of the XMM-Newton data is distributed across the Virtual Organization (VO constituted by three different research centres: ESAC (European Space Astronomy Centre, ESTEC (the European Space research and TEchnology Centre and UCM (Complutense University of Madrid. The proposed application workflow adjusts well to the Grid environment, making use of the massive parallel resources in a flexible and adaptive fashion.
Liao, Bolin; Zhang, Yunong; Jin, Long
2016-02-01
In this paper, a new Taylor-type numerical differentiation formula is first presented to discretize the continuous-time Zhang neural network (ZNN), and obtain higher computational accuracy. Based on the Taylor-type formula, two Taylor-type discrete-time ZNN models (termed Taylor-type discrete-time ZNNK and Taylor-type discrete-time ZNNU models) are then proposed and discussed to perform online dynamic equality-constrained quadratic programming. For comparison, Euler-type discrete-time ZNN models (called Euler-type discrete-time ZNNK and Euler-type discrete-time ZNNU models) and Newton iteration, with interesting links being found, are also presented. It is proved herein that the steady-state residual errors of the proposed Taylor-type discrete-time ZNN models, Euler-type discrete-time ZNN models, and Newton iteration have the patterns of O(h(3)), O(h(2)), and O(h), respectively, with h denoting the sampling gap. Numerical experiments, including the application examples, are carried out, of which the results further substantiate the theoretical findings and the efficacy of Taylor-type discrete-time ZNN models. Finally, the comparisons with Taylor-type discrete-time derivative model and other Lagrange-type discrete-time ZNN models for dynamic equality-constrained quadratic programming substantiate the superiority of the proposed Taylor-type discrete-time ZNN models once again.
Parallel computation of Euler and Navier-Stokes flows
International Nuclear Information System (INIS)
Swisshelm, J.M.; Johnson, G.M.; Kumar, S.P.
1986-01-01
A multigrid technique useful for accelerating the convergence of Euler and Navier-Stokes flow computations has been restructured to improve its performance on both SIMD and MIMD computers. The new algorithm allows both the construction of longer coarse-grid vectors and the multitasking of entire grids. Computational results are presented for the CDC Cyber 205, Cray X-MP, and Denelcor HEP I. 15 references
Stability properties of the Euler-Korteweg system with nonmonotone pressures
Giesselmann, Jan; Tzavaras, Athanasios
2016-01-01
We establish a relative energy framework for the Euler-Korteweg system with non-convex energy. This allows us to prove weak-strong uniqueness and to show convergence to a Cahn-Hilliard system in the large friction limit. We also use relative energy
Large Scale Simulations of the Euler Equations on GPU Clusters
Liebmann, Manfred; Douglas, Craig C.; Haase, Gundolf; Horvá th, Zoltá n
2010-01-01
The paper investigates the scalability of a parallel Euler solver, using the Vijayasundaram method, on a GPU cluster with 32 Nvidia Geforce GTX 295 boards. The aim of this research is to enable large scale fluid dynamics simulations with up to one
Isaac Newton learns Hebrew: Samuel Johnson's Nova cubi Hebræi tabella
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.
The architecture of Newton, a general-purpose dynamics simulator
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.
Classical mechanics from Newton to Einstein : a modern introduction
McCall, Martin
2011-01-01
This new edition of Classical Mechanics, aimed at undergraduate physics and engineering students, presents in a user-friendly style an authoritative approach to the complementary subjects of classical mechanics and relativity. The text starts with a careful look at Newton's Laws, before applying them in one dimension to oscillations and collisions. More advanced applications - including gravitational orbits and rigid body dynamics - are discussed after the limitations of Newton's inertial frames have been highlighted through an exposition of Einstein's Special Relativity. Examples gi
Classical mechanics on the GL(n, R) group and Euler-Calogero-Sutherland model
International Nuclear Information System (INIS)
Khvedelidze, A.M.; Mladenov, D.M.
2002-01-01
Relations between free motion on the GL + (n, R) group manifold and the dynamics of an n-particle system with spin degrees of freedom on a line interacting with a pairwise 1/sinh 2 x 'potential' (Euler-Calogero-Sutherland model) are discussed within a Hamiltonian reduction. Two kinds of reductions of the degrees of freedom are considered: that which is due to continuous invariance and that which is due to discrete symmetry. It is shown that, upon projecting onto the corresponding invariant manifolds, the resulting Hamiltonian system represents the Euler-Calogero-Sutherland model in both cases
Euler-Vector Clustering of GPS Velocities Defines Microplate Geometry in Southwest Japan
Savage, J. C.
2018-02-01
I have used Euler-vector clustering to assign 469 GEONET stations in southwest Japan to k clusters (k = 2, 3,..., 9) so that, for any k, the velocities of stations within each cluster are most consistent with rigid-block motion on a sphere. That is, I attempt to explain the raw (i.e., uncorrected for strain accumulation), 1996-2006 velocities of those 469 Global Positioning System stations by rigid motion of k clusters on the surface of a spherical Earth. Because block geometry is maintained as strain accumulates, Euler-vector clustering may better approximate the block geometry than the values of the associated Euler vectors. The microplate solution for each k is constructed by merging contiguous clusters that have closely similar Euler vectors. The best solution consists of three microplates arranged along the Nankaido Trough-Ryukyu Trench between the Amurian and Philippine Sea Plates. One of these microplates, the South Kyushu Microplate (an extension of the Ryukyu forearc into the southeast corner of Kyushu), had previously been identified from paleomagnetic rotations. Relative to ITRF2000 the three microplates rotate at different rates about neighboring poles located close to the northwest corner of Shikoku. The microplate model is identical to that proposed in the block model of Wallace et al. (2009, https://doi.org/10.1130/G2522A.1) except in southernmost Kyushu. On Shikoku and Honshu, but not Kyushu, the microplate model is consistent with that proposed in the block models of Nishimura and Hashimoto (2006, https://doi.org/10.1016/j.tecto.2006.04.017) and Loveless and Meade (2010, https://doi.org/10.1029/2008JB006248) without the low-slip-rate boundaries proposed in the latter.
XMM-Newton detects X-ray 'solar cycle' in distant star
2004-05-01
The Sun as observed by SOHO hi-res Size hi-res: 708 Kb The Sun as observed by SOHO The Sun as observed by the ESA/NASA SOHO observatory near the minimum of the solar cycle (left) and near its maximum (right). The signs of solar activity near the maximum are clearly seen. New XMM-Newton observations suggest that this behaviour may be typical of stars like the Sun, such as HD 81809 in the constellation Hydra. Solar flare - 4 November 2003 The huge flare produced on 4 November 2003 This image of the Sun, obtained by the ESA/NASA SOHO observatory, shows the powerful X-ray flare that took place on 4 November 2003. The associated coronal mass ejection, coming out of the Sun at a speed of 8.2 million kilometres per hour, hit the Earth several hours later and caused disruptions to telecommunication and power distribution lines. New XMM-Newton observations suggest that this behaviour may be typical of stars like the Sun, such as HD 81809 in the constellation Hydra. Since the time Galileo discovered sunspots, in 1610, astronomers have measured their number, size and location on the disc of the Sun. Sunspots are relatively cooler areas on the Sun that are observed as dark patches. Their number rises and falls with the level of activity of the Sun in a cycle of about 11 years. When the Sun is very active, large-scale phenomena take place, such as the flares and coronal mass ejections observed by the ESA/NASA solar observatory SOHO. These events release a large amount of energy and charged particles that hit the Earth and can cause powerful magnetic storms, affecting radio communications, power distribution lines and even our weather and climate. During the solar cycle, the X-ray emission from the Sun varies by a large amount (about a factor of 100) and is strongest when the cycle is at its peak and the surface of the Sun is covered by the largest number of spots. ESA's X-ray observatory, XMM-Newton, has now shown for the first time that this cyclic X-ray behaviour is common to
A Line Search Multilevel Truncated Newton Algorithm for Computing the Optical Flow
Directory of Open Access Journals (Sweden)
Lluís Garrido
2015-06-01
Full Text Available We describe the implementation details and give the experimental results of three optimization algorithms for dense optical flow computation. In particular, using a line search strategy, we evaluate the performance of the unilevel truncated Newton method (LSTN, a multiresolution truncated Newton (MR/LSTN and a full multigrid truncated Newton (FMG/LSTN. We use three image sequences and four models of optical flow for performance evaluation. The FMG/LSTN algorithm is shown to lead to better optical flow estimation with less computational work than both the LSTN and MR/LSTN algorithms.
Singh, S L; Singh, S B; Ghatak, K P
2018-04-01
In this paper an attempt is made to study the 2D Fermi Level Mass (FLM) in accumulation and inversion layers of nano MOSFET devices made of nonlinear optical, III-V, ternary, Quaternary, II-VI, IV-VI, Ge and stressed materials by formulating 2D carrier dispersion laws on the basis of k → ⋅ p → ⋅ formalism and considering the energy band constants of a particular material. It is observed taking accumulation and inversion layers of Cd3As2, CdGeAs2, InSb, Hg1-xCdxTe and In1-xGaxAsyP1-y lattice matched to InP, CdS, GaSb and Ge as examples that the FLM depends on sub band index for nano MOSFET devices made of Cd3As2 and CdGeAs2 materials which is the characteristic features such 2D systems. Besides, the FLM depends on the scattering potential in all the cases and the same mass changes with increasing surface electric field. The FLM exists in the band gap which is impossible without heavy doping.
An Error Estimate for Symplectic Euler Approximation of Optimal Control Problems
Karlsson, Jesper; Larsson, Stig; Sandberg, Mattias; Szepessy, Anders; Tempone, Raul
2015-01-01
This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading-order term consisting of an error density that is computable from symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading-error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations. The performance is illustrated by numerical tests.
Energy Technology Data Exchange (ETDEWEB)
Suescun D, D.; Oviedo T, M., E-mail: daniel.suescun@usco.edu.co [Universidad Surcolombiana, Av. Pastrana Borrero - Carrera 1, Neiva, Huila (Colombia)
2017-09-15
In this paper, a numerical study of stochastic differential equations that describe the kinetics in a nuclear reactor is presented. These equations, known as the stochastic equations of punctual kinetics they model temporal variations in neutron population density and concentrations of deferred neutron precursors. Because these equations are probabilistic in nature (since random oscillations in the neutrons and population of precursors were considered to be approximately normally distributed, and these equations also possess strong coupling and stiffness properties) the proposed method for the numerical simulations is the Euler-Maruyama scheme that provides very good approximations for calculating the neutron population and concentrations of deferred neutron precursors. The method proposed for this work was computationally tested for different seeds, initial conditions, experimental data and forms of reactivity for a group of precursors and then for six groups of deferred neutron precursors at each time step with 5000 Brownian movements per seed. In a paper reported in the literature, the Euler-Maruyama method was proposed, but there are many doubts about the reported values, in addition to not reporting the seed used, so in this work is expected to rectify the reported values. After taking the average of the different seeds used to generate the pseudo-random numbers the results provided by the Euler-Maruyama scheme will be compared in mean and standard deviation with other methods reported in the literature and results of the deterministic model of the equations of the punctual kinetics. This comparison confirms in particular that the Euler-Maruyama scheme is an efficient method to solve the equations of stochastic point kinetics but different from the values found and reported by another author. The Euler-Maruyama method is simple and easy to implement, provides acceptable results for neutron population density and concentration of deferred neutron precursors and
Regularity and energy conservation for the compressible Euler equations
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Gwiazda, P.; Swierczewska-Gwiazda, A.; Wiedemann, E.
2017-01-01
Roč. 223, č. 3 (2017), s. 1375-1395 ISSN 0003-9527 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible Euler equations Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 2.392, year: 2016 http://link.springer.com/article/10.1007%2Fs00205-016-1060-5
Weak solutions for Euler systems with non-local interactions
Czech Academy of Sciences Publication Activity Database
Carrillo, J. A.; Feireisl, Eduard; Gwiazda, P.; Swierczewska-Gwiazda, A.
2017-01-01
Roč. 95, č. 3 (2017), s. 705-724 ISSN 0024-6107 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Euler system * dissipative solutions * Newtonian interaction Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.895, year: 2016 http://onlinelibrary.wiley.com/doi/10.1112/jlms.12027/abstract
NON-INVASIVE INVERSE PROBLEM IN CIVIL ENGINEERING
Directory of Open Access Journals (Sweden)
Jan Havelka
2017-11-01
Full Text Available In this contribution we focus on recovery of spatial distribution of material parameters utilizing only non-invasive boundary measurements. Such methods has gained its importance as imaging techniques in medicine, geophysics or archaeology. We apply similar principles for non-stationary heat transfer in civil engineering. In oppose to standard technique which rely on external loading devices, we assume the natural fluctuation of temperature throughout day and night can provide sufficient information to recover the underlying material parameters. The inverse problem was solved by a modified regularised Gauss-Newton iterative scheme and the underlying forward problem is solved with a finite element space-time discretisation. We show a successful reconstruction of material parameters on a synthetic example with real measurements. The virtual experiment also reveals the insensitivity to practical precision of sensor measurements.
A non-linear multigrid method for the steady Euler equations
Hemker, P.W.; Koren, B.; Dervieux, A.; Leer, van B.; Periaux, J.; Rizzi, A.
1989-01-01
Higher-order accurate Euler-flow solutions are presented for some airfoil test cases. Second-order accurate solutions are computed by an Iterative Defect Correction process. For two test cases even higher accuracy is obtained by the additional use of a ~xtrapolation technique. Finite volume
Euler-Lagrange modeling of the hydrodynamics of dense multiphase flows
Padding, J.T.; Deen, N.G.; Peters, E. A. J. F.; Kuipers, J. A. M.
2015-01-01
The large-scale hydrodynamic behavior of relatively dense dispersed multiphase flows, such as encountered in fluidized beds, bubbly flows, and liquid sprays, can be predicted efficiently by use of Euler-Lagrange models. In these models, grid-averaged equations for the continuous-phase flow field are
An Archival Chandra and XMM-Newton Survey of Type 2 Quasars
Jia, Jianjun; Ptak, Andrew Francis; Heckman, Timothy; Zakamska, Nadia L.
2013-01-01
In order to investigate obscuration in high-luminosity type 2 active galactic nuclei (AGNs), we analyzed Chandra and XMM-Newton archival observations for 71 type 2 quasars detected at 0.05 100 eV in the rest frame) and we detect this line in the other sources through a joint fit (spectral stacking). The correlation between the Fe K alpha and [O III] fluxes and the inverse correlation of the equivalent width of the Fe Ka line with the ratio of hard X-ray and [O III] fluxes is consistent with previous results for lower luminosity Seyfert 2 galaxies. We conclude that obscuration is the cause of the weak hard X-ray emission rather than intrinsically low X-ray luminosities. We find that about half of the population of optically selected type 2 quasars are likely to be Compton thick. We also find no evidence that the amount of X-ray obscuration depends on the AGN luminosity (over a range of more than three orders of magnitude in luminosity).
Variational nature, integration, and properties of Newton reaction path.
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.
Variational nature, integration, and properties of Newton reaction path
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.
Leonhardi Euleri Opera omnia: Editing the works and correspondence of Leonhard Euler
Directory of Open Access Journals (Sweden)
Andreas KLEINERT
2015-12-01
Full Text Available The paper gives an overview on the history and present state of the edition of the complete works of Leonhard Euler (1707–1783. After several failed initiatives in the 19th century, the project began in 1907 with the edition of Euler’s printed works. The works were divided into three series: I. Mathematics (29 volumes; II. Mechanics and Astronomy (31 volumes; and III. Physics and Miscellaneous (12 volumes. After several ups and downs due to two World Wars and economic problems, the publication of the printed works with a total of 72 volumes is nearly finished. Only two volumes on perturbation theory in astronomy are still missing. The publication of series IV (manuscripts and correspondence started in 1967 as a joint project of the Swiss and the Soviet academies of sciences. The manuscript edition was postponed, and the project focussed on Euler’s correspondence which contains approximately 3000 letters, 1000 of them written by Euler. The correspondents include famous mathematicians of the 18th century like d’Alembert, Clairaut and the Bernoullis, but also many less-known people with whom Euler corresponded on a great variety of subjects. A major problem is to find and to finance appropriate editors who are able to read French, Latin, and the old German handwriting, and who are acquainted with history, culture and science of the 18th century. During the last 50 years, the editors gathered copies or scans of most of the preserved Euler’s letters. The original letters addressed to Euler were made available to the editorial group in Switzerland by the Russian Academy of Sciences before World War I, and before their restitution in 1947 the editors made fairly good photographs that are now an important part of the material basis of the edition. Each volume of the letter series (VIA contains Euler’s correspondence with one or more of his contemporaries, presented in a chronological order. Up to the present day, four volumes of the
A novel numerical flux for the 3D Euler equations with general equation of state
Toro, Eleuterio F.
2015-09-30
Here we extend the flux vector splitting approach recently proposed in (E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, 2012). The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both space and time through application of the semi-discrete ADER methodology on general meshes. The resulting methods are systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems. Formal high accuracy is assessed through convergence rates studies for schemes of up to 4th order of accuracy in both space and time on unstructured meshes.
Newton's constant from a minimal length: additional models
International Nuclear Information System (INIS)
Sahlmann, Hanno
2011-01-01
We follow arguments of Verlinde (2010 arXiv:1001.0785 [hep-th]) and Klinkhamer (2010 arXiv:1006.2094 [hep-th]), and construct two models of the microscopic theory of a holographic screen that allow for the thermodynamical derivation of Newton's law, with Newton's constant expressed in terms of a minimal length scale l contained in the area spectrum of the microscopic theory. One of the models is loosely related to the quantum structure of surfaces and isolated horizons in loop quantum gravity. Our investigation shows that the conclusions reached by Klinkhamer regarding the new length scale l seem to be generic in all their qualitative aspects.
A Non-smooth Newton Method for Multibody Dynamics
International Nuclear Information System (INIS)
Erleben, K.; Ortiz, R.
2008-01-01
In this paper we deal with the simulation of rigid bodies. Rigid body dynamics have become very important for simulating rigid body motion in interactive applications, such as computer games or virtual reality. We present a novel way of computing contact forces using a Newton method. The contact problem is reformulated as a system of non-linear and non-smooth equations, and we solve this system using a non-smooth version of Newton's method. One of the main contribution of this paper is the reformulation of the complementarity problems, used to model impacts, as a system of equations that can be solved using traditional methods.
Teaching Newton's Third Law of Motion in the Presence of Student Preconception
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.
Batina, John T.
1990-01-01
Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.
POEMS in Newton's Aerodynamic Frustum
Sampedro, Jaime Cruz; Tetlalmatzi-Montiel, Margarita
2010-01-01
The golden mean is often naively seen as a sign of optimal beauty but rarely does it arise as the solution of a true optimization problem. In this article we present such a problem, demonstrating a close relationship between the golden mean and a special case of Newton's aerodynamical problem for the frustum of a cone. Then, we exhibit a parallel…
Local Convergence and Radius of Convergence for Modified Newton Method
Directory of Open Access Journals (Sweden)
Măruşter Ştefan
2017-12-01
Full Text Available We investigate the local convergence of modified Newton method, i.e., the classical Newton method in which the derivative is periodically re-evaluated. Based on the convergence properties of Picard iteration for demicontractive mappings, we give an algorithm to estimate the local radius of convergence for considered method. Numerical experiments show that the proposed algorithm gives estimated radii which are very close to or even equal with the best ones.
Automatic interpretation of magnetic data using Euler deconvolution with nonlinear background
Digital Repository Service at National Institute of Oceanography (India)
Dewangan, P.; Ramprasad, T.; Ramana, M.V.; Desa, M.; Shailaja, B.
are close to each other. A possible solution to these problems is prposed by simultaneously estimating the source location, depth and structural index assuming nonlinear background. The Euler equation is solved in a nonlinear fashion using the optimization...
How Two Differing Portraits of Newton Can Teach Us about the Cultural Context of Science
Tucci, Pasquale
2015-01-01
Like several scientists, Isaac Newton has been represented many times over many different periods, and portraits of Newton were often commissioned by the scientist himself. These portraits tell us a lot about the scientist, the artist and the cultural context. This article examines two very different portraits of Newton that were realized more…
An addendum to the Heisenberg-Euler effective action beyond one loop
Energy Technology Data Exchange (ETDEWEB)
Gies, Holger; Karbstein, Felix [Helmholtz-Institut Jena,Fröbelstieg 3, 07743 Jena (Germany); Theoretisch-Physikalisches Institut, Abbe Center of Photonics,Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena (Germany)
2017-03-21
We study the effective interactions of external electromagnetic fields induced by fluctuations of virtual particles in the vacuum of quantum electrodynamics. Our main focus is on these interactions at two-loop order. We discuss in detail the emergence of the renowned Heisenberg-Euler effective action from the underlying microscopic theory of quantum electrodynamics, emphasizing its distinction from a standard one-particle irreducible effective action. In our explicit calculations we limit ourselves to constant and slowly varying external fields, allowing us to adopt a locally constant field approximation. One of our main findings is that at two-loop order there is a finite one-particle reducible contribution to the Heisenberg-Euler effective action in constant fields, which was previously assumed to vanish. In addition to their conceptual significance, our results are relevant for high-precision probes of quantum vacuum nonlinearity in strong electromagnetic fields.
Free time minimizers for the three-body problem
Moeckel, Richard; Montgomery, Richard; Sánchez Morgado, Héctor
2018-03-01
Free time minimizers of the action (called "semi-static" solutions by Mañe in International congress on dynamical systems in Montevideo (a tribute to Ricardo Mañé), vol 362, pp 120-131, 1996) play a central role in the theory of weak KAM solutions to the Hamilton-Jacobi equation (Fathi in Weak KAM Theorem in Lagrangian Dynamics Preliminary Version Number 10, 2017). We prove that any solution to Newton's three-body problem which is asymptotic to Lagrange's parabolic homothetic solution is eventually a free time minimizer. Conversely, we prove that every free time minimizer tends to Lagrange's solution, provided the mass ratios lie in a certain large open set of mass ratios. We were inspired by the work of Da Luz and Maderna (Math Proc Camb Philos Soc 156:209-227, 1980) which showed that every free time minimizer for the N-body problem is parabolic and therefore must be asymptotic to the set of central configurations. We exclude being asymptotic to Euler's central configurations by a second variation argument. Central configurations correspond to rest points for the McGehee blown-up dynamics. The large open set of mass ratios are those for which the linearized dynamics at each Euler rest point has a complex eigenvalue.
Energy Technology Data Exchange (ETDEWEB)
Yamasaki, N; Nanba, M; Tashiro, K [Kyushu University, Fukuoka (Japan). Faculty of Engineering
1996-03-27
Comparison study between solutions of a linear potential theory and numerical solution of Euler equations was made for flow in a supersonic through-flow fan. In numerical fluid dynamic technique, Euler equations are solved by finite difference method under the assumption of air and perfect gas fluid, and neglected viscosity and thermal conductivity of fluid. As a result, in a linear potential theory, expansion wave was regarded as equipotential discontinuous surface, while in Euler numerical solution, it was regarded as finite pressure gradient where a wave front fans out toward downstream. The latter reflection point of shock wave on a wing existed upstream as compared with the former reflection point. The shock wave angle was dominated by Euler equations, and different from the Mach line of a linear potential theory in both angle and discontinuous quantities in front and behind. Both calculated solutions well agreed with each other until the first reflection point of the Mach line, however, thereafter the difference between them increased toward downstream. 5 refs., 5 figs., 1 tab.
International Nuclear Information System (INIS)
Nesseris, Savvas; Blake, Chris; Davis, Tamara; Parkinson, David
2011-01-01
We constrain the evolution of Newton's constant using the growth rate of large-scale structure measured by the WiggleZ Dark Energy Survey in the redshift range 0.1 m (assuming General Relativity), and use this to construct a diagnostic to detect the presence of an evolving Newton's constant. Secondly we directly measure the evolution of Newton's constant, G eff , that appears in Modified Gravity theories, without assuming General Relativity to be true. The novelty of these approaches are that, contrary to other methods, they do not require knowledge of the expansion history of the Universe, H(z), making them model independent tests. Our constraints for the second derivative of Newton's constant at the present day, assuming it is slowly evolving as suggested by Big Bang Nucleosynthesis constraints, using the WiggleZ data is G double-dot eff (t 0 ) = −1.19 ± 0.95·10 −20 h 2 yr −2 , where h is defined via H 0 = 100 h km s −1 Mpc −1 , while using both the WiggleZ and the Sloan Digital Sky Survey Luminous Red Galaxy (SDSS LRG) data is G double-dot eff (t 0 ) = −3.6 ± 6.8·10 −21 h 2 yr −2 , both being consistent with General Relativity. Finally, our constraint for the rms mass fluctuation σ 8 using the WiggleZ data is σ 8 = 0.75 ± 0.08, while using both the WiggleZ and the SDSS LRG data σ 8 = 0.77 ± 0.07, both in good agreement with the latest measurements from the Cosmic Microwave Background radiation
Chaotic dynamics of flexible Euler-Bernoulli beams
Energy Technology Data Exchange (ETDEWEB)
Awrejcewicz, J., E-mail: awrejcew@p.lodz.pl [Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland and Department of Vehicles, Warsaw University of Technology, 84 Narbutta St., 02-524 Warsaw (Poland); Krysko, A. V., E-mail: anton.krysko@gmail.com [Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov (Russian Federation); Kutepov, I. E., E-mail: iekutepov@gmail.com; Zagniboroda, N. A., E-mail: tssrat@mail.ru; Dobriyan, V., E-mail: Dobriy88@yandex.ru; Krysko, V. A., E-mail: tak@san.ru [Department of Mathematics and Modeling, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov (Russian Federation)
2013-12-15
Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c{sup 2}) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions is carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q{sub 0} and frequency ω{sub p} of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.
A gravitação universal na filosofia da natureza de Isaac Newton
Garcia, Valdinei Gomes
2010-01-01
Resumo: Esta pesquisa apresenta um estudo sobre o conceito de força gravitacional na filosofia da natureza de Isaac Newton. O presente texto foi elaborado a partir dos argumentos desenvolvidos por Newton para defender esse conceito em sua obra mais importante, o Philosophiae Naturalis Principia Mathematica (1687). Será visto que, em tais argumentos, Newton restringe o conceito de força gravitacional a partir de um tratamento matemático, que ele próprio elaborou em sua obra. Por outro lado, Ne...
British physics Newton's law of funding
2007-01-01
In Britain, fundamental physics is in a pickle ISAAC NEWTON, besides being the founder of modern physics, was also master of Britain's mint. That is a precedent which many British physicists must surely wish had become traditional. At the moment, money for physics is in short supply in Britain.
Measure-valued solutions to the complete Euler system revisited
Czech Academy of Sciences Publication Activity Database
Březina, J.; Feireisl, Eduard
2018-01-01
Roč. 69, č. 3 (2018), č. článku 57. ISSN 0044-2275 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Euler system * measure-valued solution * vanishing dissipation limit Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.687, year: 2016 https://link.springer.com/article/10.1007/s00033-018-0951-8
Uniqueness of rarefaction waves in multidimensional compressible Euler system
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Kreml, Ondřej
2015-01-01
Roč. 12, č. 3 (2015), s. 489-499 ISSN 0219-8916 R&D Projects: GA ČR GA13-00522S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible Euler system * uniqueness * rarefaction wave * Riemann problem Subject RIV: BA - General Mathematics Impact factor: 0.556, year: 2015 http://www.worldscientific.com/doi/abs/10.1142/S0219891615500149
Solution of the inverse scattering problem at fixed energy with non-physical S matrix elements
International Nuclear Information System (INIS)
Eberspaecher, M.; Amos, K.; Apagyi, B.
1999-12-01
The quantum mechanical inverse elastic scattering problem is solved with the modified Newton-Sabatier method. A set of S matrix elements calculated from a realistic analytic optical model potential serves as input data. It is demonstrated that the quality of the inversion potential can be improved by including non-physical S matrix elements to half, quarter and eighth valued partial waves if the original set does not contain enough information to determine the interaction potential. We demonstrate that results can be very sensitive to the choice of those non-physical S matrix values both with the analytic potential model and in a real application in which the experimental cross section for the symmetrical scattering system of 12 C+ 12 C at E=7.998 MeV is analyzed
The Cooling Law and the Search for a Good Temperature Scale, from Newton to Dalton
Besson, Ugo
2011-01-01
The research on the cooling law began with an article by Newton published in 1701. Later, many studies were performed by other scientists confirming or confuting Newton's law. This paper presents a description and an interpretation of Newton's article, provides a short overview of the research conducted on the topic during the 18th century, and…
The Schrödinger–Newton equation and its foundations
International Nuclear Information System (INIS)
Bahrami, Mohammad; Großardt, André; Donadi, Sandro; Bassi, Angelo
2014-01-01
The necessity of quantising the gravitational field is still subject to an open debate. In this paper we compare the approach of quantum gravity, with that of a fundamentally semi-classical theory of gravity, in the weak-field non-relativistic limit. We show that, while in the former case the Schrödinger equation stays linear, in the latter case one ends up with the so-called Schrödinger–Newton equation, which involves a nonlinear, non-local gravitational contribution. We further discuss that the Schrödinger–Newton equation does not describe the collapse of the wave-function, although it was initially proposed for exactly this purpose. Together with the standard collapse postulate, fundamentally semi-classical gravity gives rise to superluminal signalling. A consistent fundamentally semi-classical theory of gravity can therefore only be achieved together with a suitable prescription of the wave-function collapse. We further discuss, how collapse models avoid such superluminal signalling and compare the nonlinearities appearing in these models with those in the Schrödinger–Newton equation. (paper)
Bohlin transformation: the hidden symmetry that connects Hooke to Newton
International Nuclear Information System (INIS)
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. (paper)
Discovering Euler Circuits and Paths through a Culturally Relevant Lesson
Robichaux, Rebecca R.; Rodrigue, Paulette R.
2006-01-01
This article describes a middle school discrete mathematics lesson that uses the context of catching crawfish to provide students with a hands-on experience related to Euler circuits and paths. The lesson promotes mathematical communication through the use of cooperative learning as well as connections between mathematics and the real world…
Maximal dissipation and well-posedness for the compressible Euler system
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard
2014-01-01
Roč. 16, č. 3 (2014), s. 447-461 ISSN 1422-6928 EU Projects: European Commission(XE) 320078 - MATHEF Keywords : maximal dissipation * compressible Euler system * weak solution Subject RIV: BA - General Mathematics Impact factor: 1.186, year: 2014 http://link.springer.com/article/10.1007/s00021-014-0163-8
[Isaac Newton's Anguli Contactus method].
Wawrzycki, Jarosław
2014-01-01
In this paper we discuss the geometrical method for calculating the curvature of a class of curves from the third Book of Isaac Newton's Principia. The method involves any curve which is generated from an elementary curve (actually from any curve whose curvature we known of) by means of transformation increasing the polar angular coordinate in a constant ratio, but unchanging the polar radial angular coordinate.
Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry
International Nuclear Information System (INIS)
Alvarez, Pedro D.; Gomis, Joaquim; Kamimura, Kiyoshi; Plyushchay, Mikhail S.
2008-01-01
We investigate the planar anisotropic harmonic oscillator with explicit rotational symmetry as a particle model with non-commutative coordinates. It includes the exotic Newton-Hooke particle and the non-commutative Landau problem as special, isotropic and maximally anisotropic, cases. The system is described by the same (2+1)-dimensional exotic Newton-Hooke symmetry as in the isotropic case, and develops three different phases depending on the values of the two central charges. The special cases of the exotic Newton-Hooke particle and non-commutative Landau problem are shown to be characterized by additional, so(3) or so(2,1) Lie symmetry, which reflects their peculiar spectral properties
International Nuclear Information System (INIS)
Yoon, Han Ik; Son, In Soo
2005-01-01
In this paper, we studied about the effect of the open crack and a tip mass on the dynamic behavior of a cantilever pipe conveying fluid with a moving mass. The equation of motion is derived by using Lagrange's equation and analyzed by numerical method. The cantilever pipe is modelled by the Euler-Bernoulli beam theory. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The influences of the crack, the moving mass, the tip mass and its moment of inertia, the velocity of fluid, and the coupling of these factors on the vibration mode, the frequency, and the tip-displacement of the cantilever pipe are analytically clarified
Verbiest, J. P. W.; Bailes, M.; van Straten, W.; Hobbs, G. B.; Edwards, R. T.; Manchester, R. N.; Bhat, N. D. R.; Sarkissian, J. M.; Jacoby, B. A.; Kulkarni, S. R.
2008-05-01
Analysis of 10 years of high-precision timing data on the millisecond pulsar PSR J0437-4715 has resulted in a model-independent kinematic distance based on an apparent orbital period derivative, dot Pb , determined at the 1.5% level of precision (Dk = 157.0 +/- 2.4 pc), making it one of the most accurate stellar distance estimates published to date. The discrepancy between this measurement and a previously published parallax distance estimate is attributed to errors in the DE200 solar system ephemerides. The precise measurement of dot Pb allows a limit on the variation of Newton's gravitational constant, |Ġ/G| <= 23 × 10-12 yr-1. We also constrain any anomalous acceleration along the line of sight to the pulsar to |a⊙/c| <= 1.5 × 10-18 s-1 at 95% confidence, and derive a pulsar mass, mpsr = 1.76 +/- 0.20 M⊙, one of the highest estimates so far obtained.
Isaac Newton Institute of Chile: The fifteenth anniversary of its "Yugoslavia" Branch
Dimitrijević, M. S.
In 2002, the Isaac Newton Institute of Chile established in Belgrade its "Yugoslavia" Branch, one of 15 branches in nine countries in Eastern Europe and Eurasia. On the occasion of fifteen years since its foundation, the activities of "Yugoslavia" Branch of the Isaac Newton Institute of Chile are briefly reviewed.
On the estimation variance for the specific Euler-Poincaré characteristic of random networks.
Tscheschel, A; Stoyan, D
2003-07-01
The specific Euler number is an important topological characteristic in many applications. It is considered here for the case of random networks, which may appear in microscopy either as primary objects of investigation or as secondary objects describing in an approximate way other structures such as, for example, porous media. For random networks there is a simple and natural estimator of the specific Euler number. For its estimation variance, a simple Poisson approximation is given. It is based on the general exact formula for the estimation variance. In two examples of quite different nature and topology application of the formulas is demonstrated.
Rietbroek, R.; Uebbing, B.; Lück, C.; Kusche, J.
2017-12-01
Ocean mass content (OMC) change due to the melting of the ice-sheets in Greenland and Antarctica, melting of glaciers and changes in terrestrial hydrology is a major contributor to present-day sea level rise. Since 2002, the GRACE satellite mission serves as a valuable tool for directly measuring the variations in OMC. As GRACE has almost reached the end of its lifetime, efforts are being made to utilize the Swarm mission for the recovery of low degree time-variable gravity fields to bridge a possible gap until the GRACE-FO mission and to fill up periods where GRACE data was not existent. To this end we compute Swarm monthly normal equations and spherical harmonics that are found competitive to other solutions. In addition to directly measuring the OMC, combination of GRACE gravity data with altimetry data in a global inversion approach allows to separate the total sea level change into individual mass-driven and steric contributions. However, published estimates of OMC from the direct and inverse methods differ not only depending on the time window, but also are influenced by numerous post-processing choices. Here, we will look into sources of such differences between direct and inverse approaches and evaluate the capabilities of Swarm to derive OMC. Deriving time series of OMC requires several processing steps; choosing a GRACE (and altimetry) product, data coverage, masks and filters to be applied in either spatial or spectral domain, corrections related to spatial leakage, GIA and geocenter motion. In this study, we compare and quantify the effects of the different processing choices of the direct and inverse methods. Our preliminary results point to the GIA correction as the major source of difference between the two approaches.
The Newtonian Moment - Isaac Newton and the Making of Modern Culture
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.
Delprat, Alejandra; Negre, Bàrbara; Puig, Marta; Ruiz, Alfredo
2009-11-18
Transposable elements (TEs) are responsible for the generation of chromosomal inversions in several groups of organisms. However, in Drosophila and other Dipterans, where inversions are abundant both as intraspecific polymorphisms and interspecific fixed differences, the evidence for a role of TEs is scarce. Previous work revealed that the transposon Galileo was involved in the generation of two polymorphic inversions of Drosophila buzzatii. To assess the impact of TEs in Drosophila chromosomal evolution and shed light on the mechanism involved, we isolated and sequenced the two breakpoints of another widespread polymorphic inversion from D. buzzatii, 2z(3). In the non inverted chromosome, the 2z(3) distal breakpoint was located between genes CG2046 and CG10326 whereas the proximal breakpoint lies between two novel genes that we have named Dlh and Mdp. In the inverted chromosome, the analysis of the breakpoint sequences revealed relatively large insertions (2,870-bp and 4,786-bp long) including two copies of the transposon Galileo (subfamily Newton), one at each breakpoint, plus several other TEs. The two Galileo copies: (i) are inserted in opposite orientation; (ii) present exchanged target site duplications; and (iii) are both chimeric. Our observations provide the best evidence gathered so far for the role of TEs in the generation of Drosophila inversions. In addition, they show unequivocally that ectopic recombination is the causative mechanism. The fact that the three polymorphic D. buzzatii inversions investigated so far were generated by the same transposon family is remarkable and is conceivably due to Galileo's unusual structure and current (or recent) transpositional activity.
Parallel computing techniques for rotorcraft aerodynamics
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).
Constraints on decaying Dark Matter from XMM-Newton observations of M31
Boyarsky, Alexey; Ruchayskiy, Oleg; Savchenko, Vladimir
2007-01-01
We derive constraints on parameters of the radiatively decaying Dark Matter (DM) particles, using XMM-Newton EPIC spectra of the Andromeda galaxy (M31). Using the observations of the outer (5'-13') parts of M31 we improve the existing constraints. For the case of sterile neutrino DM, combining our constraints with the latest computation of abundances of sterile neutrino in the Dodelson-Widrow (DW) scenario, we obtain the lower mass limit m_s 5.6 kev), we argue that the scenario in which all the DM is produced via DW mechanism is ruled out. We discuss however other production mechanisms and note that the sterile neutrino remains a viable candidate of Dark Matter, either warm or cold.
Stability of periodic steady-state solutions to a non-isentropic Euler-Poisson system
Liu, Cunming; Peng, Yue-Jun
2017-06-01
We study the stability of periodic smooth solutions near non-constant steady-states for a non-isentropic Euler-Poisson system without temperature damping term. The system arises in the theory of semiconductors for which the doping profile is a given smooth function. In this stability problem, there are no special restrictions on the size of the doping profile, but only on the size of the perturbation. We prove that small perturbations of periodic steady-states are exponentially stable for large time. For this purpose, we introduce new variables and choose a non-diagonal symmetrizer of the full Euler equations to recover dissipation estimates. This also allows to make the proof of the stability result very simple and concise.
A two-stage method for inverse medium scattering
Ito, Kazufumi
2013-03-01
We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from noisy near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer support, and one resolution enhancing step with nonsmooth mixed regularization. The first step is strictly direct and of sampling type, and it faithfully detects the scatterer support. The second step is an innovative application of nonsmooth mixed regularization, and it accurately resolves the scatterer size as well as intensities. The nonsmooth model can be efficiently solved by a semi-smooth Newton-type method. Numerical results for two- and three-dimensional examples indicate that the new approach is accurate, computationally efficient, and robust with respect to data noise. © 2012 Elsevier Inc.
Newton, Goethe and the process of perception: an approach to design
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.
On the motion of incompressible inhomogeneous Euler-Korteweg fluids
Czech Academy of Sciences Publication Activity Database
Bulíček, M.; Feireisl, Eduard; Málek, J.; Shvydkoy, R.
2010-01-01
Roč. 3, č. 3 (2010), s. 497-515 ISSN 1937-1632 R&D Projects: GA MŠk LC06052; GA ČR GA201/09/0917 Institutional research plan: CEZ:AV0Z10190503 Keywords : Korteweg fluid * inhomogeneous Euler fluid * Korteweg stress * local-in-time well-posedness * smooth solution Subject RIV: BA - General Mathematics http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5226
Directory of Open Access Journals (Sweden)
Shirmohammadi Adel
2006-10-01
Full Text Available Abstract Background Quantification of in-vivo biomolecule mass transport and reaction rate parameters from experimental data obtained by Fluorescence Recovery after Photobleaching (FRAP is becoming more important. Methods and results The Osborne-Moré extended version of the Levenberg-Marquardt optimization algorithm was coupled with the experimental data obtained by the Fluorescence Recovery after Photobleaching (FRAP protocol, and the numerical solution of a set of two partial differential equations governing macromolecule mass transport and reaction in living cells, to inversely estimate optimized values of the molecular diffusion coefficient and binding rate parameters of GFP-tagged glucocorticoid receptor. The results indicate that the FRAP protocol provides enough information to estimate one parameter uniquely using a nonlinear optimization technique. Coupling FRAP experimental data with the inverse modeling strategy, one can also uniquely estimate the individual values of the binding rate coefficients if the molecular diffusion coefficient is known. One can also simultaneously estimate the dissociation rate parameter and molecular diffusion coefficient given the pseudo-association rate parameter is known. However, the protocol provides insufficient information for unique simultaneous estimation of three parameters (diffusion coefficient and binding rate parameters owing to the high intercorrelation between the molecular diffusion coefficient and pseudo-association rate parameter. Attempts to estimate macromolecule mass transport and binding rate parameters simultaneously from FRAP data result in misleading conclusions regarding concentrations of free macromolecule and bound complex inside the cell, average binding time per vacant site, average time for diffusion of macromolecules from one site to the next, and slow or rapid mobility of biomolecules in cells. Conclusion To obtain unique values for molecular diffusion coefficient and
One hundred years of pressure hydrostatics from Stevin to Newton
Chalmers, Alan F
2017-01-01
This monograph investigates the development of hydrostatics as a science. In the process, it sheds new light on the nature of science and its origins in the Scientific Revolution. Readers will come to see that the history of hydrostatics reveals subtle ways in which the science of the seventeenth century differed from previous periods. The key, the author argues, is the new insights into the concept of pressure that emerged during the Scientific Revolution. This came about due to contributions from such figures as Simon Stevin, Pascal, Boyle and Newton. The author compares their work with Galileo and Descartes, neither of whom grasped the need for a new conception of pressure. As a result, their contributions to hydrostatics were unproductive. The story ends with Newton insofar as his version of hydrostatics set the subject on its modern course. He articulated a technical notion of pressure that was up to the task. Newton compared the mathematical way in hydrostatics and the experimental way, and sided with t...
Newton Decatur AL water sample polyfluor compound discovery
U.S. Environmental Protection Agency — All the pertinent information for recreation of the published (hopefully) tables and figures. This dataset is associated with the following publication: Newton, S.,...
Directory of Open Access Journals (Sweden)
Agung Wahyu Nurcahyo
2017-07-01
Full Text Available The purpose of this study was to describe the increase in problem-solving abilities Newton's laws of motion and students' perceptions of cooperative problem solving (CPS learning. Analysis of the data is based on the student's written answers to the five problems, the results of questionnaires and interviews. This study concluded that: (1 learning CPS make a strong impact (d-effect size = 1.81 to increase problem-solving ability of students Newton's laws of motion, (2 cooperation in the learning group CPS makes the problem easier to solve and misconceptions can be corrected. Tujuan penelitian ini adalah mendeskripsikan peningkatan kemampuan pemecahan masalah hukum gerak Newton, kesulitan yang dialami, dan persepsi mahasiswa terhadap pembelajaran cooperative problem solving (CPS. Analisa data didasarkan pada jawaban tertulis mahasiswa terhadap lima permasalahan, hasil angket dan wawancara. Penelitian ini berkesimpulan bahwa (1 pembelajaran CPS memberikan dampak yang kuat (d-effect size=1,81 terhadap peningkatan kemampuan pemecahan masalah hukum gerak Newton mahasiswa dan (2 kerjasama kelompok dalam pembelajaran CPS membuat permasalahan lebih mudah dipecahkan dan miskonsepsi dapat diperbaiki.
A Fast Newton-Shamanskii Iteration for a Matrix Equation Arising from M/G/1-Type Markov Chains
Directory of Open Access Journals (Sweden)
Pei-Chang Guo
2017-01-01
Full Text Available For the nonlinear matrix equations arising in the analysis of M/G/1-type and GI/M/1-type Markov chains, the minimal nonnegative solution G or R can be found by Newton-like methods. We prove monotone convergence results for the Newton-Shamanskii iteration for this class of equations. Starting with zero initial guess or some other suitable initial guess, the Newton-Shamanskii iteration provides a monotonically increasing sequence of nonnegative matrices converging to the minimal nonnegative solution. A Schur decomposition method is used to accelerate the Newton-Shamanskii iteration. Numerical examples illustrate the effectiveness of the Newton-Shamanskii iteration.
Application of Quasi-Newton methods to the analysis of axisymmetric pressure vessels
International Nuclear Information System (INIS)
Parisi, D.A.C.
1987-01-01
This work studies the application of Quasi-Newton techniques to material nonlinear analysis of axisymmetrical pressure vessels by the finite element method. In the formulation the material bahavior is described by an isotropic elastoplastic model with strain hardening. The continum is discretized through triangular finite elements of axisymmetrical solids with linear interpolation of the displacement field. The incremental governing equations are derived by the virtual work. The solution of the system of simultaneous nonlinear equations is solved iteratively by the Quasi-Newton method employing the BFGS update. The numerical performance of the proposed method is compared with the Newton-Raphson method and some of its variants through some selected examples. (author) [pt
Different seeds to solve the equations of stochastic point kinetics using the Euler-Maruyama method
International Nuclear Information System (INIS)
Suescun D, D.; Oviedo T, M.
2017-09-01
In this paper, a numerical study of stochastic differential equations that describe the kinetics in a nuclear reactor is presented. These equations, known as the stochastic equations of punctual kinetics they model temporal variations in neutron population density and concentrations of deferred neutron precursors. Because these equations are probabilistic in nature (since random oscillations in the neutrons and population of precursors were considered to be approximately normally distributed, and these equations also possess strong coupling and stiffness properties) the proposed method for the numerical simulations is the Euler-Maruyama scheme that provides very good approximations for calculating the neutron population and concentrations of deferred neutron precursors. The method proposed for this work was computationally tested for different seeds, initial conditions, experimental data and forms of reactivity for a group of precursors and then for six groups of deferred neutron precursors at each time step with 5000 Brownian movements per seed. In a paper reported in the literature, the Euler-Maruyama method was proposed, but there are many doubts about the reported values, in addition to not reporting the seed used, so in this work is expected to rectify the reported values. After taking the average of the different seeds used to generate the pseudo-random numbers the results provided by the Euler-Maruyama scheme will be compared in mean and standard deviation with other methods reported in the literature and results of the deterministic model of the equations of the punctual kinetics. This comparison confirms in particular that the Euler-Maruyama scheme is an efficient method to solve the equations of stochastic point kinetics but different from the values found and reported by another author. The Euler-Maruyama method is simple and easy to implement, provides acceptable results for neutron population density and concentration of deferred neutron precursors and
Magnetic Levitation and Newton's Third Law
Aguilar, Horacio Munguia
2007-01-01
Newton's third law is often misunderstood by students and even their professors, as has already been pointed out in the literature. Application of the law in the context of electromagnetism can be especially problematic, because the idea that the forces of "action" and "reaction" are equal and opposite independent of the medium through which they…
Isaac Newton and the Royal Mint
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 11; Issue 12. Isaac Newton and the Royal Mint. Biman Nath. Article-in-a-Box Volume 11 Issue 12 December 2006 pp 6-7. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/011/12/0006-0007 ...
The importance of being equivalent: Newton's two models of one-body motion
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
Gower, Robert M.
2018-02-12
We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive definite matrices in such a way that all iterates (approximate solutions) generated by the algorithm are positive definite matrices themselves. This opens the way for many applications in the field of optimization and machine learning. As an application of our general theory, we develop the {\\\\em first accelerated (deterministic and stochastic) quasi-Newton updates}. Our updates lead to provably more aggressive approximations of the inverse Hessian, and lead to speed-ups over classical non-accelerated rules in numerical experiments. Experiments with empirical risk minimization show that our rules can accelerate training of machine learning models.
Accuracy of an unstructured-grid upwind-Euler algorithm for the ONERA M6 wing
Batina, John T.
1991-01-01
Improved algorithms for the solution of the three-dimensional, time-dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured-grid flow solvers. The spatial discretization involves a flux-split approach that is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time-integration scheme using a multistage Runge-Kutta procedure or an implicit time-integration scheme using a Gauss-Seidel relaxation procedure, which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady flow results are presented for both the NACA 0012 airfoil and the Office National d'Etudes et de Recherches Aerospatiales M6 wing to demonstrate applications of the new Euler solvers. The paper presents a description of the Euler solvers along with results and comparisons that assess the capability.
Energy Technology Data Exchange (ETDEWEB)
Chafi, Fatima Zohra; Halle, Stephane [Mechanical engineering department, Ecole de technologie superieure, Quebec university, 1100 rue Notre-Dame Ouest, Montreal, Quebec H3C 1K3 (Canada)
2011-02-15
This paper presents the results of a study that consists of estimating the temperature distribution and air flow movement in a model room with a numerical model based on the Euler equations. Numerical results obtained for two scenarios of ventilation and heating are compared with the predictions of a Navier-Stokes model, as well as with experimental results. A comparison of the local thermal comfort indices PMV and PPD obtained experimentally and numerically is also presented. Results show that the Euler model is capable of properly estimating the temperature distribution, the air movement and the comfort indices in the room. Furthermore, the use of Euler equations allows a reduction of computational time in the order of 30% compared to the Navier-Stokes modeling. (author)
Twisted Acceleration-Enlarged Newton-Hooke Hopf Algebras
International Nuclear Information System (INIS)
Daszkiewicz, M.
2010-01-01
Ten Abelian twist deformations of acceleration-enlarged Newton-Hooke Hopf algebra are considered. The corresponding quantum space-times are derived as well. It is demonstrated that their contraction limit τ → ∞ leads to the new twisted acceleration-enlarged Galilei spaces. (author)
Wang, Feiyan; Morten, Jan Petter; Spitzer, Klaus
2018-05-01
In this paper, we present a recently developed anisotropic 3-D inversion framework for interpreting controlled-source electromagnetic (CSEM) data in the frequency domain. The framework integrates a high-order finite-element forward operator and a Gauss-Newton inversion algorithm. Conductivity constraints are applied using a parameter transformation. We discretize the continuous forward and inverse problems on unstructured grids for a flexible treatment of arbitrarily complex geometries. Moreover, an unstructured mesh is more desirable in comparison to a single rectilinear mesh for multisource problems because local grid refinement will not significantly influence the mesh density outside the region of interest. The non-uniform spatial discretization facilitates parametrization of the inversion domain at a suitable scale. For a rapid simulation of multisource EM data, we opt to use a parallel direct solver. We further accelerate the inversion process by decomposing the entire data set into subsets with respect to frequencies (and transmitters if memory requirement is affordable). The computational tasks associated with each data subset are distributed to different processes and run in parallel. We validate the scheme using a synthetic marine CSEM model with rough bathymetry, and finally, apply it to an industrial-size 3-D data set from the Troll field oil province in the North Sea acquired in 2008 to examine its robustness and practical applicability.
Derivation of the Euler equations in Thomas-Fermi theories of a hot nuclear system
International Nuclear Information System (INIS)
Wang, C.
1992-01-01
The variational extreme condition with respect to statistical distribution of nucleons in momentum space is applied to derive the Euler equation of the nuclear density profile. The resultant Euler equation of the nuclear density profile is proven to be identical with that obtained in the usual Thomas-Fermi theories of a hot nuclear system where the variation is made with respect to the nuclear density profile. A Fermi-Dirac-type distribution appears as a result of variation in the present approach, while it is used as a given expression in obtaining the variation of the nuclear density profile in the usual Thomas-Fermi theories
The cooling law and the search for a good temperature scale, from Newton to Dalton
International Nuclear Information System (INIS)
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 discusses the relationships between the research on cooling laws and the definition of a temperature scale, as it was treated in Newton's article and in the work of Dalton, including Dalton's search for the absolute zero of temperature. It is shown that these scientists considered the exponential cooling law as a fundamental principle rather than a conjecture to be tested by means of experiments. The faith in the simplicity of natural laws and the spontaneous idea of proportionality between cause and effect seem to have strongly influenced Newton and Dalton. The topic is developed in a way that can be suitable for both undergraduate students and general physicists.
Newton solution of inviscid and viscous problems
International Nuclear Information System (INIS)
Venkatakrishnan, V.
1988-01-01
The application of Newton iteration to inviscid and viscous airfoil calculations is examined. Spatial discretization is performed using upwind differences with split fluxes. The system of linear equations which arises as a result of linearization in time is solved directly using either a banded matrix solver or a sparse matrix solver. In the latter case, the solver is used in conjunction with the nested dissection strategy, whose implementation for airfoil calculations is discussed. The boundary conditions are also implemented in a fully implicit manner, thus yielding quadratic convergence. Complexities such as the ordering of cell nodes and the use of a far field vortex to correct freestream for a lifting airfoil are addressed. Various methods to accelerate convergence and improve computational efficiency while using Newton iteration are discussed. Results are presented for inviscid, transonic nonlifting and lifting airfoils and also for laminar viscous cases. 17 references
Inverse isotope effect in iron-based superconductor
International Nuclear Information System (INIS)
Shirage, Parasharam M.; Kihou, Kunihiro; Miyazawa, Kiichi; Lee, Chul-Ho; Kito, Hijiri; Yoshida, Yoshiyuki; Eisaki, Hiroshi; Tanaka, Yasumoto; Iyo, Akira
2010-01-01
We have found that (Ba, K)Fe 2 As 2 superconductor (a transition temperature, T c ∼ 38 K) shows an inverse Iron isotope effect (α Fe = -0.18 ± 0.03, where T c ∼ M -αFe and M is the iron isotope mass), i.e. the sample containing the larger iron mass depicts higher T c . Systematic studies using three types of Fe-isotopes ( 54 Fe, natural Fe and 57 Fe) reveal a clear inverse shift on T c by measurements of temperature dependent magnetization and resistivity. The inverse isotope effect that is the first case in high-T c superconductors strongly suggests that superconducting mechanism of the iron-based system is not explained by conventional BCS theory mediated by phonons.
Analysis of A Uniform Bernoulli – Euler Beam on Winkler Foundation ...
African Journals Online (AJOL)
ADOWIE PERE
2018-03-09
Mar 9, 2018 ... method to analyze Winkler foundation subjected to a harmonic moving load on a uniform Bernoulli – Euler Beam. MATLAB software was used to implement the Newmark time integration method to ... A lot of engineering structures under moving loads .... Because numerical procedure produce stability issue,.
A Hybrid Parallel Preconditioning Algorithm For CFD
Barth,Timothy J.; Tang, Wei-Pai; Kwak, Dochan (Technical Monitor)
1995-01-01
A new hybrid preconditioning algorithm will be presented which combines the favorable attributes of incomplete lower-upper (ILU) factorization with the favorable attributes of the approximate inverse method recently advocated by numerous researchers. The quality of the preconditioner is adjustable and can be increased at the cost of additional computation while at the same time the storage required is roughly constant and approximately equal to the storage required for the original matrix. In addition, the preconditioning algorithm suggests an efficient and natural parallel implementation with reduced communication. Sample calculations will be presented for the numerical solution of multi-dimensional advection-diffusion equations. The matrix solver has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The full paper will show numerous examples in CFD to demonstrate the efficiency and robustness of the method.
Directory of Open Access Journals (Sweden)
E. A. Venter
1964-03-01
Full Text Available Die geweldige oplewing van die Christelike wetenskaps- gedagte in ons geeslose tyd, is ongetwyfeld ’n haas onverklaar- bare verskynsel. Dwarsdeur die eeue het Christene ook wetenskap beoefen saam met ongelowiges, maar dit was eers in ons leeftyd dat die principia van die Christelike religie ook vrugbaar gemaak is vir die wetenskapsbeoefening. In hierdie verband sal die name van Dooyeweerd, Vollenhoven, Stoker e.a. steeds met eer vermeld word. Natuurlik het belydende Christene ook voorheen wel deeglik saamgewerk aan die gebou van die wetenskap. Die intieme verband tussen religie, wysbegeerte en wetenskaps beoefening is toe egter nog nie suiwer ingesien nie. Uit hier die tydperk dateer die arbeid van sir Isaac Newton.
Behera, Laxmi; Chakraverty, S.
2014-03-01
Vibration analysis of nonlocal nanobeams based on Euler-Bernoulli and Timoshenko beam theories is considered. Nonlocal nanobeams are important in the bending, buckling and vibration analyses of beam-like elements in microelectromechanical or nanoelectromechanical devices. Expressions for free vibration of Euler-Bernoulli and Timoshenko nanobeams are established within the framework of Eringen's nonlocal elasticity theory. The problem has been solved previously using finite element method, Chebyshev polynomials in Rayleigh-Ritz method and using other numerical methods. In this study, numerical results for free vibration of nanobeams have been presented using simple polynomials and orthonormal polynomials in the Rayleigh-Ritz method. The advantage of the method is that one can easily handle the specified boundary conditions at the edges. To validate the present analysis, a comparison study is carried out with the results of the existing literature. The proposed method is also validated by convergence studies. Frequency parameters are found for different scaling effect parameters and boundary conditions. The study highlights that small scale effects considerably influence the free vibration of nanobeams. Nonlocal frequency parameters of nanobeams are smaller when compared to the corresponding local ones. Deflection shapes of nonlocal clamped Euler-Bernoulli nanobeams are also incorporated for different scaling effect parameters, which are affected by the small scale effect. Obtained numerical solutions provide a better representation of the vibration behavior of short and stubby micro/nanobeams where the effects of small scale, transverse shear deformation and rotary inertia are significant.
An A Posteriori Error Estimate for Symplectic Euler Approximation of Optimal Control Problems
Karlsson, Peer Jesper
2015-01-07
This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian system connected with the optimal control problem. The error representation has a leading order term consisting of an error density that is computable from Symplectic Euler solutions. Under an assumption of the pathwise convergence of the approximate dual function as the maximum time step goes to zero, we prove that the remainder is of higher order than the leading error density part in the error representation. With the error representation, it is possible to perform adaptive time stepping. We apply an adaptive algorithm originally developed for ordinary differential equations.
De las Leyes de Newton a la Guerra de Troya
Plastino, Ángel Ricardo
2014-01-01
La publicación en 1687 del libro Philosophia Naturalis Principia Mathematica por Issac Newton marcó un importante hito en la historia del pensamiento humano. Sobre la base de tres sencillos principios de movimiento y de la ley de gravitación universal, y mediante razonamientos matemáticos, Newton logró explicar y unificar dentro de un esquema conceptual coherente una gran cantidad de fenómenos naturales: el movimiento de los planetas, las mareas, la forma de la Tierra, entre otros. Más aún, N...
Bouchaala, Adam M.
2016-12-05
We present a method to determine accurately the position and mass of an entity attached to the surface of an electrostatically actuated clamped-clamped microbeam implemented as a mass sensor. In the theoretical investigation, the microbeam is modeled as a nonlinear Euler-Bernoulli beam and a perturbation technique is used to develop a closed-form expression for the frequency shift due to an added mass at a specific location on the microbeam surface. The experimental investigation was conducted on a microbeam made of Polyimide with a special lower electrode to excite both of the first and second modes of vibration. Using an ink-jet printer, we deposited droplets of polymers with a defined mass and position on the surface of the microbeam and we measured the shifts in its resonance frequencies. The theoretical predictions of the mass and position of the deposited droplets match well with the experimental measurements.
Bouchaala, Adam M.; Nayfeh, Ali H.; Jaber, Nizar; Younis, Mohammad I.
2016-01-01
We present a method to determine accurately the position and mass of an entity attached to the surface of an electrostatically actuated clamped-clamped microbeam implemented as a mass sensor. In the theoretical investigation, the microbeam is modeled as a nonlinear Euler-Bernoulli beam and a perturbation technique is used to develop a closed-form expression for the frequency shift due to an added mass at a specific location on the microbeam surface. The experimental investigation was conducted on a microbeam made of Polyimide with a special lower electrode to excite both of the first and second modes of vibration. Using an ink-jet printer, we deposited droplets of polymers with a defined mass and position on the surface of the microbeam and we measured the shifts in its resonance frequencies. The theoretical predictions of the mass and position of the deposited droplets match well with the experimental measurements.
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.
International Nuclear Information System (INIS)
Dai, Yang; Borisov, Alexey B.; Boyer, Keith; Rhodes, Charles K.
2000-01-01
The construction of inverse states in a finite field F P α enables the organization of the mass scale with fundamental octets in an eight-dimensional index space that identifies particle states with residue class designations. Conformance with both CPT invariance and the concept of supersymmetry follows as a direct consequence of this formulation. Based on two parameters (P α and g α ) that are anchored on a concordance of physical data, this treatment leads to (1) a prospective mass for the muon neutrino of approximately27.68 meV, (2) a value of the unified strong-electroweak coupling constant α* = (34.26) -1 that is physically defined by the ratio of the electron neutrino and muon neutrino masses, and (3) a see-saw congruence connecting the Higgs, the electron neutrino, and the muon neutrino masses. Specific evaluation of the masses of the corresponding supersymmetric Higgs pair reveals that both particles are superheavy (> 10 18 GeV). No renormalization of the Higgs masses is introduced, since the calculational procedure yielding their magnitudes is intrinsically divergence-free. Further, the Higgs fulfills its conjectured role through the see-saw relation as the particle defining the origin of all particle masses, since the electron and muon neutrino systems, together with their supersymmetric partners, are the generators of the mass scale and establish the corresponding index space. Finally, since the computation of the Higgs masses is entirely determined by the modulus of the field P α , which is fully defined by the large-scale parameters of the universe through the value of the universal gravitational constant G and the requirement for perfect flatness (Omega = 1.0), the see-saw congruence fuses the concepts of mass and space and creates a new unified archetype
Non-relativistic conformal symmetries and Newton-Cartan structures
International Nuclear Information System (INIS)
Duval, C; Horvathy, P A
2009-01-01
This paper provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton-Cartan spacetime. The Lie algebras of non-relativistic conformal transformations are introduced via the Galilei structure. They form a family of infinite-dimensional Lie algebras labeled by a rational 'dynamical exponent', z. The Schroedinger-Virasoro algebra of Henkel et al corresponds to z = 2. Viewed as projective Newton-Cartan symmetries, they yield, for timelike geodesics, the usual Schroedinger Lie algebra, for which z = 2. For lightlike geodesics, they yield, in turn, the Conformal Galilean Algebra (CGA) of Lukierski, Stichel and Zakrzewski (alias 'alt' of Henkel), with z = 1. Physical systems realizing these symmetries include, e.g. classical systems of massive and massless non-relativistic particles, and also hydrodynamics, as well as Galilean electromagnetism.
pyGIMLi: An open-source library for modelling and inversion in geophysics
Rücker, Carsten; Günther, Thomas; Wagner, Florian M.
2017-12-01
Many tasks in applied geosciences cannot be solved by single measurements, but require the integration of geophysical, geotechnical and hydrological methods. Numerical simulation techniques are essential both for planning and interpretation, as well as for the process understanding of modern geophysical methods. These trends encourage open, simple, and modern software architectures aiming at a uniform interface for interdisciplinary and flexible modelling and inversion approaches. We present pyGIMLi (Python Library for Inversion and Modelling in Geophysics), an open-source framework that provides tools for modelling and inversion of various geophysical but also hydrological methods. The modelling component supplies discretization management and the numerical basis for finite-element and finite-volume solvers in 1D, 2D and 3D on arbitrarily structured meshes. The generalized inversion framework solves the minimization problem with a Gauss-Newton algorithm for any physical forward operator and provides opportunities for uncertainty and resolution analyses. More general requirements, such as flexible regularization strategies, time-lapse processing and different sorts of coupling individual methods are provided independently of the actual methods used. The usage of pyGIMLi is first demonstrated by solving the steady-state heat equation, followed by a demonstration of more complex capabilities for the combination of different geophysical data sets. A fully coupled hydrogeophysical inversion of electrical resistivity tomography (ERT) data of a simulated tracer experiment is presented that allows to directly reconstruct the underlying hydraulic conductivity distribution of the aquifer. Another example demonstrates the improvement of jointly inverting ERT and ultrasonic data with respect to saturation by a new approach that incorporates petrophysical relations in the inversion. Potential applications of the presented framework are manifold and include time
Directory of Open Access Journals (Sweden)
Suci Furwati
2017-08-01
Full Text Available Abstract: Students who have good conceptual acquisition will be able to represent the concept by using multi representation. This study aims to determine the improvement of students' understanding of the concept of Newton's Law material, and the quality of representation used in solving problems on Newton's Law material. The results showed that the concept acquisition of students increased from the average of 35.32 to 78.97 with an effect size of 2.66 (strong and N-gain of 0.68 (medium. The quality of each type of student representation also increased from level 1 and level 2 up to level 3. Key Words: concept aquisition, represetation quality, multi representation learning, Newton’s Law Abstrak: Siswa yang memiliki penguasaan konsep yang baik akan mampu merepresentasikan konsep dengan menggunakan multi representasi. Penelitian ini bertujuan untuk mengetahui peningkatan pemahaman konsep siswa SMP pada materi Hukum Newton, dan kualitas representasi yang digunakan dalam menyelesaikan masalah pada materi Hukum Newton. Hasil penelitian menunjukkan bahwa penguasaan konsep siswa meningkat dari rata-rata 35,32 menjadi 78,97 dengan effect size sebesar 2,66 (kuat dan N-gain sebesar 0,68 (sedang. Kualitas tiap jenis representasi siswa juga mengalami peningkatan dari level 1 dan level 2 naik menjadi level 3. Kata kunci: hukum Newton, kualitas representasi, pemahaman konsep, pembelajaran multi representasi
Preconditioned Inexact Newton for Nonlinear Sparse Electromagnetic Imaging
Desmal, Abdulla; Bagci, Hakan
2014-01-01
with smoothness promoting optimization/regularization schemes. However, this type of regularization schemes are known to perform poorly when applied in imagining domains with sparse content or sharp variations. In this work, an inexact Newton algorithm
Smooth values of the iterates of the Euler's Phi function
Lamzouri, Youness
2005-01-01
Let $\\phi(n)$ be the Euler-phi function, define $\\phi_0(n) = n$ and $\\phi_{k+1}(n)=\\phi(\\phi_{k}(n))$ for all $k\\geq 0$. We will determine an asymptotic formula for the set of integers $n$ less than $x$ for which $\\phi_k(n)$ is $y$-smooth, conditionally on a weak form of the Elliott-Halberstam conjecture.
Integration with respect to the Euler characteristic and its applications
Energy Technology Data Exchange (ETDEWEB)
Gusein-Zade, Sabir M [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)
2010-09-16
The notion of integration with respect to the Euler characteristic and its generalizations are discussed: integration over the infinite-dimensional spaces of arcs and functions, motivic integration. The author describes applications of these notions to the computation of monodromy zeta functions, Poincare series of multi-index filtrations, generating series of classes of certain moduli spaces, and so on. Bibliography: 70 titles.