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Spectral line polarization with angle-dependent partial frequency redistribution

K. N. Nagendra, M. Sampoorna
2011 Astronomy and Astrophysics  
The SEM is shown to be 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).  ... 
doi:10.1051/0004-6361/201117491 fatcat:es463uj2w5b43enb2pitkever4

Spectral line polarization with angle-dependent partial frequency redistribution

M. Sampoorna
2011 Astronomy and Astrophysics  
We introduce a single scattering 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.  ... 
doi:10.1051/0004-6361/201116866 fatcat:w37ijokl5vfy5fkkqwhbfpuleq

Parametrization of the angular distribution of Cherenkov light in air showers

Luan B. Arbeletche, Vitor de Souza
2021 European Physical Journal C: Particles and Fields  
Yet, no description of this phenomenon is available covering both regions of small and large 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  ... 
doi:10.1140/epjc/s10052-021-08971-7 fatcat:hdz7tuwiorc73aynbbbeyxhtf4

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  ... 

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

H. Al Kazwini, Q. Agobert, A. Siebert, B. Famaey, G. Monari, S. Rozier, P. Ramos, R. Ibata, S. Gausland, C. Riviere, D. Spolyar
2021 arXiv   pre-print
First, we use better estimates for the action-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.  ... 
arXiv:2012.06597v2 fatcat:64ncxdb3fndbljncfs3zqnxw6i

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.  ... 

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  ... 

Page 625 of Astronomy and Astrophysics Vol. 248, Issue 2 [page]

1991 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?  ... 

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.  ... 

Hanle effect with angle-dependent partial redistribution

K. N. Nagendra, H. Frisch, M. Faurobert
2002 Astronomy and Astrophysics  
We show that it is necessary to incorporate 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.  ... 
doi:10.1051/0004-6361:20021349 fatcat:fzlhuujukjfjri4scdcjj3hziq

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  ... 

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)  ... 

Particle Filter Implementation [chapter]

Samuel Davey, Neil Gordon, Ian Holland, Mark Rutten, Jason Williams
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  ... 
doi:10.1007/978-981-10-0379-0_8 fatcat:6pvggnnhvbfuphxthqtsrado6a

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?  ... 

Unit Reynolds number, Mach number and pressure gradient effects on laminar–turbulent transition in two-dimensional boundary layers

Steffen Risius, Marco Costantini, Stefan Koch, Stefan Hein, Christian Klein
2018 Experiments in Fluids  
Furthermore, the receptivity coefficients dependence on incidence 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).  ... 
doi:10.1007/s00348-018-2538-8 fatcat:ztwxmkgftnehvft2wnp7oughxq
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