Dynamics of charged particles and magnetic dipoles around magnetized quasi-Schwarzschild black holes

In the present paper, we have investigated the motion of charged particles together with magnetic dipoles to determine how well the spacetime deviation parameter $$\epsilon $$ ϵ and external uniform magnetic field can mimic the spin of a rotating Kerr black hole. Investigation of charged particle motion has shown that the deviation parameter $$\epsilon $$ ϵ in the absence of an external magnetic fields can mimic the rotation parameter of the Kerr spacetime up to $$a/M \approx 0.5$$ a / M ≈ 0.5 . The combination of an external magnetic field and deviation parameter can do even a better job mimicking the rotation parameter up to $$a/M\simeq 0.93$$ a / M ≃ 0.93 , which corresponds to the rapidly rotating case. Study of the dynamics of the magnetic dipoles around quasi-Schwarzschild black holes in the external magnetic field has shown that there are degeneracy values of the ISCO radius of test particles at $$\epsilon _{cr}>\epsilon \ge 0.35$$ ϵ cr > ϵ ≥ 0.35 which may lead to two different values of the innermost stable circular orbit (ISCO) radius. When the deviation parameter is in the range of $$\epsilon \in (-1,\ 1)$$ ϵ ∈ ( - 1 , 1 ) , it can mimic the spin of a rotating Kerr black hole in the range $$a/M \in (0.0537, \ 0.3952)$$ a / M ∈ ( 0.0537 , 0.3952 ) for magnetic dipoles with values of the magnetic coupling parameter $$\beta \in [-0.25,\ 0.25]$$ β ∈ [ - 0.25 , 0.25 ] in corotating orbits.

Structural diversity in pyridine and polypyridine adducts of ring slipped manganocene: correlating ligand steric bulk with quantified deviation from ideal hapticity

The observed deviation from idealized hapticity of new and known MnCp2-adduct complexes correlates with a deviation parameter and steric bulk.

Remarks on the geometric parameters in describing diffraction optics of asymmetric Bragg crystals

This communication gives the asymmetric factor b and deviation parameter η describing the diffraction geometry in a more general way including very asymmetric scattering arrangements. Darwin's parameter Y defined on the dispersion surface and the associated deviation parameter ηY given by the Takagi–Taupin equations are proposed to characterize the angular deviation from the exact resonance of Bragg diffraction. With respect to ηY of a high accuracy, the validity of conventional forms of the deviation parameter is further discussed.

An Improved Estimator of σ in Quality Control

We present a new estimator for the standard deviation parameter in the standard quality control model. We argue that it has a smaller mean square error than the usual estimator when the data are normal and that, unlike the usual estimator, it remains consistent even when the data are not normal.

An improved deviation parameter for the simulation of dynamical X-ray diffraction on epitaxic heterostructures

X-ray diffraction rocking curves of a strained-layer superlattice structure have been measured at symmetric and asymmetric Bragg reflections and compared with simulated diffraction curves. The calculations are based on dynamical scattering theory. The experimental and theoretical curves exhibit a discrepancy with regard to the angular position of the higher-order satellite reflections, which can be removed by introducing a new expression for the deviation parameter in the dynamical diffraction theory. The improved deviation parameter extends the range of validity of the two-beam approximation, especially for asymmetric reflections with glancing exit geometry. Therefore, if the relaxation of strained-layer heterostructures is to be determined by comparison with simulated rocking curves, only the improved parameter should be used.