scholarly journals A Comparison between Second-Order Post-Newtonian Hamiltonian and Coherent Post-Newtonian Lagrangian in Spinning Compact Binaries

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 584
Author(s):  
Xu-Hui Cheng ◽  
Guo-Qing Huang
Keyword(s):  
Binary Systems ◽  
Equations Of Motion ◽  
Exact Result ◽  
Spin Coupling ◽  
Spin Orbit Coupling ◽  
Compact Binaries ◽  
Numerical Investigations ◽  
Compact Binary ◽  
The Difference ◽  
Spin Spin Coupling

In relativistic celestial mechanics, post-Newtonian (PN) Lagrangian and PN Hamiltonian formulations are not equivalent to the same PN order as our previous work in PRD (2015). Usually, an approximate Lagrangian is used to discuss the difference between a PN Hamiltonian and a PN Lagrangian. In this paper, we investigate the dynamics of compact binary systems for Hamiltonians and Lagrangians, including Newtonian, post-Newtonian (1PN and 2PN), and spin–orbit coupling and spin–spin coupling parts. Additionally, coherent equations of motion for 2PN Lagrangian are adopted here to make the comparison with Hamiltonian approaches and approximate Lagrangian approaches at the same condition and same PN order. The completely opposite nature of the dynamics shows that using an approximate PN Lagrangian is not convincing. Hence, using the coherent PN Lagrangian is necessary for obtaining an exact result in the research of dynamics of compact binary at certain PN order. Meanwhile, numerical investigations from the spinning compact binaries show that the 2PN term plays an important role in causing chaos in the PN Hamiltonian system.

scholarly journals Hunting for Dwarf Galaxies Hosting the Formation and Coalescence of Compact Binaries

Physics ◽  
2019 ◽  
Vol 1 (3) ◽  
pp. 412-429 ◽  
Author(s):  
Luca Graziani
Keyword(s):  
Binary Systems ◽  
Local Group ◽  
Dwarf Galaxies ◽  
Large Population ◽  
Compact Binaries ◽  
Compact Binary ◽  
The Galaxy ◽  
Low Metallicity ◽  
Formation And Evolution ◽  
Galaxy Assembly

Here we introduce the latest version of the GAMESH model, capable to consistently account for the formation and evolution of compact binary systems along the cosmic assembly of a Milky Way (MW)-like galaxy, centered on a local group volume resolving a large population of dwarf satellites. After describing the galaxy assembly process and how the formation of binary systems is accounted for, we summarize some recent findings on the properties and evolution of low-metallicity dwarf galaxies hosting the birth/coalescence of stellar/compact binaries generating GW150914-like signals. Finally, we focus on the mass and orbital properties of the above compact binary candidates assessing their impact on the resulting coalescence times and on selecting suitable galaxy hosts.

Through-space or proximate 19F,19F and 19F,1H spin–spin coupling constants in some benzenesulfonyl fluoride derivatives

1976 ◽  
Vol 54 (22) ◽  
pp. 3564-3568 ◽  
Author(s):  
William J. E. Parr ◽  
Ted Schaefer
Keyword(s):  
Magnetic Resonance ◽  
Proton Magnetic Resonance ◽  
Coupling Constants ◽  
Spin Coupling ◽  
Side Chain ◽  
Conformational Preference ◽  
Fluorine Nucleus ◽  
Spin Coupling Constants ◽  
The Difference ◽  
Spin Spin Coupling

The analysis of the fluorine and proton magnetic resonance spectra of 2,4,6-trimethylbenzenesulfonyl fluoride and of 2,5-difluorobenzenesulfonyl fluoride yields the signs and magnitudes of the spin–spin coupling constants containing a through-space component. The coupling between the fluorine nucleus and the methyl protons over five bonds is +1.9 Hz, opposite in sign to the −3.1 Hz observed for the corresponding coupling in 2,6-dimethylbenzoyl fluoride. The difference of 5 Hz is possibly a consequence of the different conformational preference of the SO2F and COF substituents. The coupling over four bonds between the fluorine nucleus on the side chain and that on the ring is +11.6 Hz in 2,5-difluorobenzenesulfonyl fluoride. It is argued that this value indicates a preference of the S—F bond for a plane lying, on average, nearly perpendicular to the benzene ring. Similar indications are noted for pentafluorobenzenesulfonyl fluoride and for pentafluorobenzenesulfinyl fluoride.

The mutual influence of Y···N and H···H interactions in XHY···NCH···HM complexes (X = F, Cl, Br; Y = S, Se; M = Li, Na, BeH, MgH): tuning of the chalcogen bond by dihydrogen bond interaction

2016 ◽  
Vol 94 (6) ◽  
pp. 567-573
Author(s):  
Mehdi D. Esrafili ◽  
Soheila Asadollahi ◽  
Yousef Dadban Shahamat
Keyword(s):  
Ab Initio Calculations ◽  
Ab Initio ◽  
Binary Systems ◽  
Mutual Influence ◽  
Ternary Complexes ◽  
Coupling Constants ◽  
Spin Coupling ◽  
Cooperative Effects ◽  
Bonding Properties ◽  
Spin Spin Coupling

The equilibrium structures, interaction energies, and bonding properties of ternary XHY···NCH···HM complexes are studied by ab initio calculations, where X = F, Cl, Br, Y = S, Se, and M = Li, Na, BeH, MgH. The ab initio calculations are carried out at the MP2/aug-cc-pVTZ level. The results indicate that all optimized Y···N and H···H binding distances in the ternary complexes are smaller than the corresponding values in the binary systems. The calculated cooperative energies (Ecoop) are between −0.20 kcal/mol in BrHS···NCH···HBeH and −3.29 kcal/mol in FHSe···NCH···HNa. For a given Y and M, the estimated Ecoop values increase as X = F > Cl > Br. In addition, the selenium-bonded complexes exibit larger Ecoop values than those of the sulfur-bonded counterparts. The cooperativity between Y···N and H···H interactions is further analyzed by quantum theory of atoms in molecules and natural bond orbital methods. Cooperative effects make an increase in the J(Y–N) and J(H–H) spin–spin coupling constants of the ternary complexes with respect to the binary systems.

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