scholarly journals Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation

2014 ◽  
Vol 89 (6) ◽  
Author(s):  
Abhay G. Shah ◽  
John L. Friedman ◽  
Bernard F. Whiting
Keyword(s):  
High Precision ◽  
High Order ◽  
Self Force ◽  
Force Calculation

Application of Quadratic Programming Method to Cable Force Calculation of Cable Erection Arch Bridge

2014 ◽  
Vol 587-589 ◽  
pp. 1364-1369
Author(s):  
Cheng Wu ◽  
Jin Yu Liu ◽  
Shui Xing Zhou
Keyword(s):  
Quadratic Programming ◽  
High Precision ◽  
Steel Tube ◽  
Influence Matrix ◽  
Calculation Process ◽  
Cable Force ◽  
Quadratic Programming Method ◽  
Cable Forces ◽  
Force Calculation ◽  
Number Of Iterations

Taking the bare arch deformation under gravity as target alignment, the influence matrix that associates the cable forces with segment deformation is obtained via ANSYS program, and the cable force is quickly calculated by MATLAB quadratic programming toolbox. It is illustrated with an example of Guizhou Zong-xi River Bridge, which is a 360-meter concrete filled steel tube bridge in construction, and the calculation process is given. The results show that, this new method has the advantages of high precision and less number of iterations.

scholarly journals Computation and consequences of high order amplitude- and parameter-dependent tune shifts in storage rings for high precision measurements

2019 ◽  
Vol 34 (36) ◽  
pp. 1942011 ◽  
Author(s):  
Adrian Weisskopf ◽  
David Tarazona ◽  
Martin Berz
Keyword(s):  
Phase Space ◽  
Normal Form ◽  
High Precision ◽  
Storage Ring ◽  
Differential Algebra ◽  
Storage Rings ◽  
High Order ◽  
Precision Measurements ◽  
System Parameters ◽  
Parameter Dependent

Nonlinear effects of the various electric field and magnetic field components of storage rings to confine the particles and bend their trajectory can cause substantial amplitude-dependent tune shifts within the beam. Furthermore, tune shifts are often sensitive to variations of system parameters, e.g. total particle momentum offsets [Formula: see text]. Such amplitude- and parameter-dependent tune shifts influence the dynamics and stability of a beam in particle storage rings. Thus, it is critical for high precision measurements to analyze and understand these influences. On this basis, we present normal form methods for the calculation of high order amplitude and system parameter dependencies of the horizontal and vertical tunes in storage rings using the differential algebra (DA) framework within COSY INFINITY. A storage ring is simulated using COSY INFINITY to generate a DA Poincaré return map describing the transverse phase space behavior after each revolution in the storage ring. The map is expanded around the parameter-dependent closed orbit of the system before transforming the resulting map into normal form coordinates to extract the high order tune dependencies on the phase space amplitude and variation in the system parameters. As a specific example, a storage ring similar to the Storage Ring of the Muon [Formula: see text]-2 Experiment at Fermilab (E989) is investigated.

scholarly journals High-order asymptotics for the spin-weighted spheroidal equation at large real frequency

2019 ◽  
Vol 475 (2222) ◽  
pp. 20180701
Author(s):  
Marc Casals ◽  
Adrian C. Ottewill ◽  
Niels Warburton
Keyword(s):  
Black Holes ◽  
Asymptotic Expansion ◽  
Numerical Calculation ◽  
High Precision ◽  
High Order ◽  
Eigenvalues And Eigenfunctions ◽  
Spin Field ◽  
Real Frequency ◽  
Kerr Black Holes

The spin-weighted spheroidal eigenvalues and eigenfunctions arise in the separation by variables of spin-field perturbations of Kerr black holes. We derive a large, real-frequency asymptotic expansion of the spin-weighted spheroidal eigenvalues and eigenfunctions to high order. This expansion corrects and extends existing results in the literature and we validate it via a high-precision numerical calculation.

Force Calculation of Cycloid Gear at Three Supporting Points Of Gear Pin for Speed Reducer with Three Cycloid Gears

2011 ◽  
Vol 284-286 ◽  
pp. 2409-2413
Author(s):  
Ying Shi Sun ◽  
Tian Min Guan ◽  
Xu Zhang
Keyword(s):  
High Precision ◽  
Driving Speed ◽  
Speed Reducer ◽  
Force Calculation

FA high-precision drive, namely cycloid driving speed reducer with three cycloid gears, adopts the new driving structure of three cycloid gears at eccentric angle of 120 between each other. The paper analyzes the force of cycloid gear and pin gear at three supporting points of gear pin mainly by analysis, and compares the force of cycloid gear of the speed reducers with two cycloid gears.

High-orders methods and high-precision arithmetics make direct scattering transform for the Korteweg-De Vries equation robust.

2021 ◽  
Author(s):  
Aleksandr Gudko ◽  
Andrey Gelash ◽  
Rustam Mullyadzhanov
Keyword(s):  
High Precision ◽  
Vries Equation ◽  
High Order ◽  
Scattering Data ◽  
Computational Domain ◽  
Wave Fields ◽  
Scattering Coefficients ◽  
Direct Scattering ◽  
Scattering Transform ◽  
De Vries

<p>Similar to the theory of direct scattering transform for nonlinear wave fields containing solitons within the focusing one-dimensional nonlinear Schrödinger equation [1], we revisit the theory associated with the Korteweg–De Vries equation. We study a crucial fundamental property of the scattering problem for multisoliton potentials demonstrating that in many cases position parameters of solitons cannot be identified with standard machine precision arithmetics making solitons in some sense “uncatchable”. Using the dressing method we find the landscape of soliton scattering coefficients in the plane of the complex spectral parameter for multisoliton wave fields truncated within a finite domain, allowing us to capture the nature of such anomalous numerical errors. They depend on the size of the computational domain L leading to a counterintuitive exponential divergence when increasing L in the presence of a small uncertainty in soliton eigenvalues. Then we demonstrate how one of the scattering coefficients loses its analytical properties due to the lack of the wave-field compact support in case of L→∞. Finally, we show that despite this inherent direct scattering transform feature, the wave fields of arbitrary complexity can be reliably analyzed using high-precision arithmetics and high-order algorithms based on the Magnus expansion [2, 3] providing accurate information about soliton amplitudes, velocities<span>, positions</span> and intensity of the radiation. This procedure is robust even in the presence of noise opening broad perspectives in analyzing experimental data on propagation of surface waves on shallow water.</p><p>The work is partially funded by Russian Science Foundation grant No 19-79-30075.</p><p>[1] Gelash A., Mullyadzhanov R. Anomalous errors of direct scattering transform // Physical Review E 101 (5), 052206, 2020.</p><p>[2] Mullyadzhanov R., Gelash A. Direct scattering transform of large wave packets // Optics Letters 44 (21), 5298-5301, 2019.</p><p>[3] Gudko A., Gelash A., Mullyadzhanov R. High-order numerical method for scattering data of the Korteweg—De Vries equation // Journal of Physics: Conference Series 1677 (1), 012011, 2020.</p><p> </p><p> </p>

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