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Spectral line polarization with angle-dependent partial frequency redistribution

2011
*
Astronomy and Astrophysics
*

The SEM is shown to be

doi:10.1051/0004-6361/201117491
fatcat:es463uj2w5b43enb2pitkever4
*an*efficient method to solve*angle*-dependent PRD problems involving the Hanle effect. ... Here we present*an*efficient iterative method to solve the polarized line radiative transfer equation in weak magnetic fields using*angle*-dependent PRD functions. Methods. ... We present this comparison for 1D cut-off*approximation*(*Sect*. 6.1.1),*approximation*II (*Sect*. 6.1.2), and*approximation*I (*Sect*. 6.1.3). ...##
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Spectral line polarization with angle-dependent partial frequency redistribution

2011
*
Astronomy and Astrophysics
*

We introduce a single scattering

doi:10.1051/0004-6361/201116866
fatcat:w37ijokl5vfy5fkkqwhbfpuleq
*approximation*to the problem of polarized line radiative transfer in weak magnetic fields with*an**angle*-dependent PRD. ... This helps us to rapidly compute*an**approximate*solution to the difficult and numerically expensive problem of polarized line formation with*angle*-dependent PRD. Methods. ...*N*. Nagendra for stimulating discussions and critical comments on the manuscript. Thanks are also due to L. S. Anusha for useful comments. ...##
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Parametrization of the angular distribution of Cherenkov light in air showers

2021
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European Physical Journal C: Particles and Fields
*

Yet, no description of this phenomenon is available covering both regions of small and large

doi:10.1140/epjc/s10052-021-08971-7
fatcat:hdz7tuwiorc73aynbbbeyxhtf4
*angles*to the shower axis. ... Finally, the emitted photon forms*an**angle*θ with the shower axis. ... Funded by SCOAP 3 . μ p 0,μ (±err) p 1,μ (±err) p 2,μ (±err) p 3, Appendix A: Validation of*approximations*In this Appendix the models presented in*Sect*. 2 (exact) and*Sect*. 3 (*approximated*) are compared ...##
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Page 21 of Applied Physics. A and B Vol. A34, Issue 2
[page]

1984
*
Applied Physics. A and B
*

*An*upper

*n*= 1,2, ... ... Maximum impact parameters P, (

*Sect*. 2.2) and the surface binding energy E, (

*Sect*. 2.3), are indicated. 3, is the recoil

*angle*in the laboratory system P, IMPACT PARAMETER (A) back in the laboratory system ...

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Perturbed distribution functions with accurate action estimates for the Galactic disc
[article]

2021
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arXiv
*
pre-print

First, we use better estimates for the action-

arXiv:2012.06597v2
fatcat:64ncxdb3fndbljncfs3zqnxw6i
*angle*variables away from quasi-circular orbits, computed from the AGAMA software, and we present*an*efficient routine to numerically re-express any perturbing ... In this theoretical paper we extend previous work in which, making use of the epicyclic*approximation*, the linearized Boltzmann equation had been used to explicitly compute, away from resonances, the perturbed ... The perturbing potential in actions and*angles*M16 worked in the epicyclic*approximation*as it provides*an*analytical expression for evaluating actions and*angles*from cylindrical coordinates. ...##
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Page 523 of Astronomy and Astrophysics Vol. 308, Issue 2
[page]

1996
*
Astronomy and Astrophysics
*

We perform

*an**angle*average over the frequency redistribution terms in Eq. (13) excluding the phase matrix P(*n*;*n*’). ... In*Sect*. 8 we will show, through comparisons with exact calculations made using the Monte Carlo method, that the*approximation*is, in general, excellent. ...##
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Page 442 of Astronomy and Astrophysics Vol. 297, Issue 2
[page]

1995
*
Astronomy and Astrophysics
*

and azimuthal

*angles*in the coordi- nate frame with the z-axis along the direction*n*to the observer (Fig. 1); s(E,*n*) is the local spectral intensity (depending on the strength and direction of the magnetic ... It was shown in Paper II that the*approximation*is fairly accurate for the strongly magnetized atmospheres, except for radiation*angles*6 (w.r.t. the surface normal) close to 7/2, which give a small contribution ...##
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Page 625 of Astronomy and Astrophysics Vol. 248, Issue 2
[page]

1991
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Astronomy and Astrophysics
*

In the considered wavelength region it is |

*n*' — 1|«1 and*n*” « 1, ie. it is In—1|«1. (2) Furthermore, to set*n*” = 0 is*an*acceptable*approximation*and this was done throughout the paper (see appendix B ... For small-*angle*scattering it is*n*/2 S(0,a) = ikoa? ...##
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Page 727 of Astronomy and Astrophysics Vol. 328, Issue 2
[page]

1997
*
Astronomy and Astrophysics
*

*An*erratum is given in

*Sect*. 8, follow- ing the conclusions given in

*Sect*. 7. 2. ...

*An*interesting example of Rayleigh scattering in strong magnetic field is given in

*Sect*. 6. ...

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Hanle effect with angle-dependent partial redistribution

2002
*
Astronomy and Astrophysics
*

We show that it is necessary to incorporate

doi:10.1051/0004-6361:20021349
fatcat:fzlhuujukjfjri4scdcjj3hziq
*an**angle*-dependent redistribution mechanism especially in the computation of the Stokes U parameter. ... We present a method which can solve the problem in both the levels of*approximation*. The method is based on a perturbative approach to line polarization. ...*N*. Nagendra is grateful to the scientists and other staff at the Observatoire de la Côte d'Azur (OCA), Nice, France for their warm hospitality during his visits to OCA. He is grateful to Dr. ...##
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Page 2 of Astronomy and Astrophysics Vol. 288, Issue 1
[page]

1994
*
Astronomy and Astrophysics
*

These

*approximations*are derived in*Sect*. 5 and compared with the numerical ones. ... Using the notation of SEF, the lens equation reads _fl-*n*-y7 0 uia)= ( 0 oe (& 2 2, i=1 (2.1) a, =< fi. = Ux —a,(x), |e — x,|" with K = Ke + Kx; Q, is the deflection*angle*caused by the randomly distributed ...##
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Page 177 of Astronomy and Astrophysics Vol. 184, Issue 1-2
[page]

1987
*
Astronomy and Astrophysics
*

For the case

*n*, = 3, we have (Fig. 3) Yo | Yo >3—m, + [(*n*, + 3)? + 2)". Yomax = V3 ° (*n*, - 5) (64) and for the*approximate*disk case (*n*, = 3, Fig. 2): Yomax = V6 —1% 1.4495. ... It has the form v,*N*(U, V,P,R) = M(U, V,P,R). (66) Near the sonic point (*N*= M = 0), (66) can be*approximated*by its first order expansion: VNy = My. (67) ...##
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Particle Filter Implementation
[chapter]

2016
*
SpringerBriefs in Electrical and Computer Engineering
*

*An*alternative is to

*approximate*the distribution numerically. ...

*Sect*. 6.6 Control

*angle*set point The OU parameter, denotedθ k in

*Sect*. 6.6 Instanteous control

*angle*Control

*angle*, denoted θ k in

*Sect*. 6.6 Altitude In discrete 1,000 feet steps Instantaneous ...

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Page 32 of Astronomy and Astrophysics Vol. 147, Issue 1
[page]

1985
*
Astronomy and Astrophysics
*

32

*approximation*, namely _daE o =teorr*\—ar'f j ae T€,, T) &t, + baat T(e;,*n*} (A-9) where ¢* = 5m,c? ... In*Sect*. 5 we dealt instead with*an*anisotropic situation. In the TL we used a 6 — function*approximation*for the energy of the scattered photon, with A(q/E,)= (A-13) with q, >= <8 e=t=el? ...##
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Unit Reynolds number, Mach number and pressure gradient effects on laminar–turbulent transition in two-dimensional boundary layers

2018
*
Experiments in Fluids
*

Furthermore, the receptivity coefficients dependence on incidence

doi:10.1007/s00348-018-2538-8
fatcat:ztwxmkgftnehvft2wnp7oughxq
*angle*of acoustic waves was used to correct the determined critical*N*-factors. ... Thereby, a found dependency of the determined critical*N*-factors on H 12 decreased, leading to*an*average critical*N*-factor of about 9.5 with a standard deviation of ≈ 0.8. ... Furthermore, the receptivity coefficients dependence on incidence*angle*is used to correct determined critical*N*-factors (*Sect*. 4.2). ...
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