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Utrecht, Netherlands

Tautz R.C.,Astronomical Institute Utrecht | Dominici D.,TU Berlin
Physics Letters, Section A: General, Atomic and Solid State Physics | Year: 2010

Exact expressions for certain Kapteyn series of the first and second kind are obtained. Such sums are needed in analytical theories describing Cosmic Ray scattering in turbulent magnetic fields. Also, some functions defined by sums involving derivatives of Bessel functions are considered. Numerical methods and applications of the results are discussed. © 2010 Elsevier B.V. All rights reserved. Source


Tautz R.C.,Astronomical Institute Utrecht
Plasma Physics and Controlled Fusion | Year: 2010

The problem of cosmic ray scattering in magnetohydrodynamic turbulence is revisited using a recently developed Monte Carlo simulation code. Diffusion coefficients are obtained using magnetostatic turbulence, slab Alfvénic turbulence with and without electric fields and isotropic magnetosonic turbulence with and without electric fields. All non-magnetostatic simulations are carried out for different values of the Alfvén velocity so that the effects of different particle to Alfvén velocity ratios can be studied. For slab turbulence, it is shown that Alfvén waves guarantee the recovery of diffusion, as predicted by analytical studies. The inclusion of electric fields, however, immediately leads to superdiffusion, if the Alfvén velocity is not too small. Furthermore, the energy gain through stochastic acceleration processes is investigated both qualitatively and quantitatively. The comparison with previous simulation reveals both similarities and interesting differences. © 2010 IOP Publishing Ltd. Source


Lerche I.,Martin Luther University of Halle Wittenberg | Tautz R.C.,Astronomical Institute Utrecht
Journal of Physics A: Mathematical and Theoretical | Year: 2010

In discussing the signatures available from high intensity Compton scattering, a problem of considerable interest in photon scattering from active galactic nuclei and their emission jets, Harvey et al (2009 Phys. Rev. A 79 063407) showed that the properties of some other than conventional Kapteyn series play fundamental roles in determining the spectral output both with respect to frequency and with respect to emission angle. While they were able to provide bounds to the required series in terms of known Kapteyn series that could be summed analytically in closed form, only numerical analysis could take their investigation further as they demonstrated. The purpose of this paper is to show that the many Kapteyn series involved in the scattering problem can all be reduced either to analytic form or to a single Kapteyn series that cannot be evaluated in closed form but for which an integral representation is available. This reduction is of considerable benefit in controlling the correctness and accuracy of numerical investigations; the reduction also provides significant insight into some basic procedures for summing such unconventional Kapteyn series as well as allowing a better understanding of the dependence of the scattering on the physical parameters involved than would be the case directly from the series. © 2010 IOP Publishing Ltd. Source


Yurkin M.A.,Novosibirsk State University | Min M.,Astronomical Institute Utrecht | Hoekstra A.G.,University of Amsterdam
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2010

We compared three formulations of the discrete dipole approximation (DDA) for simulation of light scattering by particles with refractive indices m=10+10i, 0.1+i, and 1.6+0.01i. These formulations include the filtered coupled dipoles (FCD), the lattice dispersion relation (LDR) and the radiative reaction correction. We compared the number of iterations required for the convergence of the iterative solver (proportional to simulation time) and the accuracy of final results. We showed that the LDR performance for m=10+10i is especially bad, while the FCD is a good option for all cases studied. Moreover, we analyzed the detailed structure of DDA errors and the spectrum of the DDA interaction matrix to understand the performance of the FCD. In particular, this spectrum, obtained with the FCD for particles smaller than the wavelength, falls into the bounds, physically implied for the spectrum of the infinite-dimensional integral scattering operator, contrary to two other DDA formulations. Finally, such extreme refractive indices can now be routinely simulated using modern desktop computers using the publicly available ADDA code, which includes an efficient implementation of the FCD. © 2010 The American Physical Society. Source


Vladilo G.,National institute for astrophysics | Abate C.,University of Trieste | Abate C.,Astronomical Institute Utrecht | Yin J.,University of Trieste | And 2 more authors.
Astronomy and Astrophysics | Year: 2011

Silicates are an important component of interstellar dust that has been poorly investigated in high redshift galaxies. As a preliminary step to studying silicates at high redshift, we survey silicon depletions in damped Ly α (DLA) systems. Silicon depletion is mild in the Galactic interstellar medium (ISM) and is expected to be weaker in most DLA systems, so we introduce a method for improving the accuracy of DLA depletion measurements. We compare abundance ratios measured in the gas with calculations of total abundance ratios of gas and dust predicted by models of galactic chemical evolution tailored for DLA systems. To tune the model parameters, we use the dust-free observational diagram S/Zn versus Zn/H, and we also compare the look back time estimated from the absorption redshift with the evolutionary time predicted by the model. By applying our method to a large set of DLA column densities, we succeeded in measuring the depletion of silicon in 74 systems. For comparison, we also measure iron and magnesium depletions (105 and 10 systems, respectively) with the same method. The mean depletion of silicon that we derive, δSi ≃ -0.27 ± 0.16 dex, is surprisingly close to that of iron, δFe ≃ -0.42 ± 0.28 dex, despite iron being much more depleted than silicon in the Galactic ISM. Silicon depletion in DLA systems does not correlate with metallicity, at variance with iron depletion, for which we confirm a rise with [Fe/H] found in previous work. Magnesium depletion seems to behave more in accordance with silicon than with iron. The different behaviors of the silicon and iron depletions suggests a complex history of dust production at the early stages of galactic chemical evolution. © 2011 ESO. Source

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