scholarly journals Higher-order spin effects in the dynamics of compact binaries. I. Equations of motion

2006 ◽  
Vol 74 (10) ◽  
Author(s):  
Guillaume Faye ◽  
Luc Blanchet ◽  
Alessandra Buonanno
Keyword(s):  
Equations Of Motion ◽  
Higher Order ◽  
Compact Binaries ◽  
Spin Effects

scholarly journals Higher-order spin effects in the dynamics of compact binaries. II. Radiation field

2006 ◽  
Vol 74 (10) ◽  
Author(s):  
Luc Blanchet ◽  
Alessandra Buonanno ◽  
Guillaume Faye
Keyword(s):  
Radiation Field ◽  
Higher Order ◽  
Compact Binaries ◽  
Spin Effects

scholarly journals Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

2021 ◽  
Vol 502 (3) ◽  
pp. 3976-3992
Author(s):  
Mónica Hernández-Sánchez ◽  
Francisco-Shu Kitaura ◽  
Metin Ata ◽  
Claudio Dalla Vecchia
Keyword(s):  
Fourth Order ◽  
Large Scale ◽  
Equations Of Motion ◽  
Large Scale Structure ◽  
Real Space ◽  
Higher Order ◽  
Second Order ◽  
Scale Structure ◽  
Integration Schemes ◽  
Reconstruction Methods

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

scholarly journals Time-domain effective-one-body gravitational waveforms for coalescing compact binaries with nonprecessing spins, tides, and self-spin effects

2018 ◽  
Vol 98 (10) ◽  
Author(s):  
Alessandro Nagar ◽  
Sebastiano Bernuzzi ◽  
Walter Del Pozzo ◽  
Gunnar Riemenschneider ◽  
Sarp Akcay ◽  
...  
Keyword(s):  
Time Domain ◽  
Compact Binaries ◽  
Spin Effects

Free Vibration of Moderately Thick Conical Shells Using a Higher Order Shear Deformable Theory

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
R. D. Firouz-Abadi ◽  
M. Rahmanian ◽  
M. Amabili
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Arbitrary Boundary ◽  
Conical Shells ◽  
First Time ◽  
Circumferential Wave ◽  
Shear Deformable

The present study considers the free vibration analysis of moderately thick conical shells based on the Novozhilov theory. The higher order governing equations of motion and the associate boundary conditions are obtained for the first time. Using the Frobenius method, exact base solutions are obtained in the form of power series via general recursive relations which can be applied for any arbitrary boundary conditions. The obtained results are compared with the literature and very good agreement (up to 4%) is achieved. A comprehensive parametric study is performed to provide an insight into the variation of the natural frequencies with respect to thickness, semivertex angle, circumferential wave numbers for clamped (C), and simply supported (SS) boundary conditions.

Modal Analysis of Multi Layer Viscoelastic Rotors Considering Higher Order Model

2013 ◽  
Author(s):  
S. Chandraker ◽  
H. Roy ◽  
G. Maurya
Keyword(s):  
Modal Analysis ◽  
Equations Of Motion ◽  
Stability Limit ◽  
Higher Order ◽  
Constitutive Relationship ◽  
Order System ◽  
Order Model ◽  
Rotor Shaft ◽  
Number Of Layers ◽  
Modal Damping

This paper involves the development of mathematical model of multilayered viscoelastic rotor using beam finite element and at the same time studying their modal analysis. The operator based constitutive relationship is used to obtain the equations of motion. The FE formulation contents higher order system where the number of order increases with the number of layers exists in the rotor shaft. Under these conditions, the complex modal behaviour of the rotor-shaft is studied to get an insight of the dynamic characteristics of the system, in terms of Modal Damping Factors, Stability Limit of Spin-speed (SLS), the directional Frequency Response Function (dFRF) as well as the direction of whirl of the shaft in different modes. Many researchers adopted this methodology for obtaining the dynamic behaviour of a second order system. This work is started by motivation of the absentia of work for higher order system.

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