China
Africa
Explore chapters and articles related to this topic
Introductory Material
Published in Ronald L. Snell, Stanley E. Kurtz, Jonathan M. Marr, Fundamentals of Radio Astronomy, 2019
Ronald L. Snell, Stanley E. Kurtz, Jonathan M. Marr
Doppler effect!relativisticWhen the relative velocity between a light source and an observer is large, we need to properly account for special relativistic effects. In particular, we need to include time dilation between the two reference frames, which causes a decrease in the observed frequency by the Lorentz factor γ. Time dilation will occur regardless of the direction of the velocity, and so the full relativistic Doppler effect formulation involves a time dilation term, which contains the magnitude of the complete velocity vector, v→, and a term due to the classical Doppler effect which involves only the radial velocity, vR. Again without derivation, the observed frequency, ν, is given by ν=1γνe1+(vR/c)=νe1−(v2/c2)1+(vR/c), where the emitted frequency is νe and γ is given by γ=11−(v2/c2). As before, the sign of the radial velocity depends on whether the light source is approaching (negative) or receding (positive). Since the relativistic formulation depends on both the radial velocity and the total velocity, without further information about the direction of motion, it is impossible to infer the radial velocity from just the measured frequency shift.
Estimation and interpretation of equilibrium scour depth around circular bridge piers by using optimized XGBoost and SHAP
Published in Engineering Applications of Computational Fluid Mechanics, 2023
Nasrin Eini, Sayed M. Bateni, Changhyun Jun, Essam Heggy, Shahab S. Band
The superiority of RPSO–XGBoost over PSO–XGBoost and RFO–XGBoost is attributed to several factors. Firstly, the RPSO technique incorporates relativistic effects, allowing particles to move at speeds that can approach the speed of light (Roder et al., 2020). These relativistic effects enable RPSO–XGBoost to explore the search space extensively, conducting a more comprehensive and thorough search for optimal hyperparameters (Roder et al., 2020). Secondly, the relativistic effects in RPSO facilitate more efficient convergence of particles towards the global optimum (Roder et al., 2020). The effective navigation of the complex search space by RPSO allows RPSO–XGBoost to reveal significant patterns and dependencies that influence scour depth, resulting in highly accurate predictions.
Low-lying electronic terms of diatomic molecules AB (A = Sc–Ni, B = Cu/Ag/Au)
Published in Molecular Physics, 2020
Davood Alizadeh Sanati, Dirk Andrae
In addition, the exact 2-component (X2C) Hamiltonian along with the Kramers-restricted configuration interaction (KRCI) approach is utilised for the atoms and for the diatomic molecules ACu. It is thereby shown that the MRCI-(SO) and the exact 2-component KRCI levels of theory yield the same electronic GSTs not only for the atoms but also for the molecules ACu. In the case of CoCu, relativistic effects are monitored through the variation of the speed of light (). Our findings indicate that spin-orbit splittings for the GSTs of ACu and AAg are smaller than those in the isolated atoms. Although it is shown that the excited terms of the transition metal atoms A can give rise to molecular terms which are more strongly bound than the GSTs, it was found for all but three diatomic molecules AB – in the absence of spin-orbit interaction – that the molecular GSTs correlate to the lowest separated atom limits A() + B(), the three exceptions being the Ni-containing molecules NiB. Overall, the terms interact with more strongly than the terms , which is perhaps due to the dominant bonding interaction. In the cases of Sc, Ti, V, Mn, Fe, Co, and Ni the configurations generate the Λ–S molecular GSTs, whereas for Cr, Cu, Ag, and Au the configurations give rise to the GSTs.
The road to Assisi
Published in Molecular Physics, 2023
Much of the 'meat' is in the chemistry of specific elements, or groups of elements, take the actinides or lanthanides, the heavy transition metals such as Os, Ir, Au, Hg or main-group metals Pb, Bi, not to speak of the superheavies. This takes us to the evergreen Periodic Table, where the differences between rows 5 and 6 (Ag/Au) mainly originate from relativistic effects, the lanthanide contraction due to filling the 4f shell, compensating for the other shell-structure effects.