Browsing by Subject "Scattering"

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  • Zinoviev, A. N.; Nordlund, K. (2017)
    The interatomic potential determines the nuclear stopping power in materials. Most ion irradiation simulation models are based on the universal-Ziegler-Biersack-Littmark (ZBL) potential (Ziegler et a1.,1983), which, however, is an average and hence may not describe the stopping of all ion-material combinations well. Here we consider pair-specific interatomic potentials determined experimentally and by density functional theory simulations with DMol approach (DMol software, 1997) to choose basic wave functions. The interatomic potentials calculated using the DMol approach demonstrate an unexpectedly good agreement with experimental data. Differences are mainly observed for heavy atom systems, which suggests they can be improved by extending a basis set and more accurately considering the relativistic effects. Experimental data prove that the approach of determining interatomic potentials from quasielastic scattering can be successfully used for modeling collision cascades in ion-solids collisions. The data obtained clearly indicate that the use of any universal potential is limited to internuclear distances R <7 a(f) (a(f) is the Firsov length). (C) 2017 Published by Elsevier B.V.
  • Holmberg, Manu (Helsingin yliopisto, 2020)
    This thesis considers certain mathematical formulation of the scattering phenomena. Scattering is a common physical process, where some initial wave is disturbed, producing a scattered wave. If the direct problem is to determine the scattered wave from the knowledge of the object that causes the scattering as well and the initial wave, then the inverse problem would be to determine the object from the knowledge on how different waves scatter from it. In this thesis we consider direct and inverse scattering problems governed by Helmholtz equation $\Delta u + k^2 \eta u = 0$ in $\mathbb{R}^d$ with $d = 3$. The positive function $\eta \in L^\infty(\mathbb{R}^d)$ is considered to be such that $\eta(x) = 1$ outside of some ball. In particular the function $\eta$ models the physical properties of the scattering object and in a certain physical setting, the function $n = +\sqrt{\eta}$ is the index of refraction. The initial motivation for this thesis was the inverse scattering problem and its uniqueness. However, for any inverse problem, one first has to understand the corresponding direct problem. In the end, the balance between treating the direct and inverse problem is left fairly even. This thesis closely follows books by Colton and Kress, and Kirsch. The first chapter is the introduction, in which the overview of the thesis is presented and the working assumptions are made. The second chapter treats the needed preliminaries, such as compact operators, Sobolev spaces, Fredholm alternative, spherical harmonics and spherical Bessel functions. In particular these are needed in various results of chapter three, in which the direct scattering problem is considered. After motivating and defining the direct scattering problem, the main goal is to prove its well-posedness. The uniqueness of the problem is proved by two results, Rellich's lemma and unique continuation principle. The Fredholm alternative is applied to prove existence of the solution on the basis of uniqueness. Equipped with the understanding of the direct scattering problem, the inverse scattering problem can be considered in the fourth chapter. After defining the inverse scattering problem, the uniqueness of the solution is considered. The proof is contrasted to the historically important paper by Calderón considering another kind of inverse problem. The proof consists of three lemmas, from which the second and third are directly used in proving the uniqueness of the inverse problem. The uniqueness of the inverse problem can be considered as the main result of this thesis.
  • Frattin, E.; Munoz, O.; Moreno, F.; Nava, J.; Escobar-Cerezo, J.; Gomez Martin, J. C.; Guirado, D.; Cellino, A.; Coll, P.; Raulin, F.; Bertini, I.; Cremonese, G.; Lazzarin, M.; Naletto, G.; La Forgia, F. (2019)
    We present experimental phase function and degree of linear polarization curves for seven samples of cometary dust analogues namely: ground pieces of Allende, DaG521, FRO95002, and FRO99040 meteorites, Mg-rich olivine and pyroxene, and a sample of organic tholins. The experimental curves have been obtained at the IAA Cosmic Dust Laboratory at a wavelength of 520 nm covering a phase angle range from 3 degrees to 175 degrees. We also provide values of the backscattering enhancement for our cometary analogue samples. The final goal of this work is to compare our experimental curves with observational data of comets and asteroids to better constrain the nature of cometary and asteroidal dust grains. All measured phase functions present the typical behaviour for mu m-sized cosmic dust grains. Direct comparison with data provided by the OSIRIS/Rosetta camera for comet 67P/Churyumov-Gerasimenko reveals significant differences and supports the idea of a coma dominated by big chunks, larger than one micrometer. The polarization curves are qualitatively similar to ground-based observations of comets and asteroids. The position of the inversion polarization angle seems to be dependent on the composition of the grains. We find opposite dependence of the maximum of the polarization curve for grains sizes in the Rayleigh-resonance and geometric optics domains, respectively.
  • Penttilä, Antti; Markkanen, Johannes; Väisänen, Timo; Räbinä, Jukka; Yurkin, Maxim; Muinonen, Karri (2021)
    We study the scattering properties of a cloud of particles. The particles are spherical, close to the incident wavelength in size, have a high albedo, and are randomly packed to 20% volume density. We show, using both numerically exact methods for solving the Maxwell equations and radiative-transfer-approximation methods, that the scattering properties of the cloud converge after about ten million particles in the system. After that, the backward-scattered properties of the system should estimate the properties of a macroscopic, practically infinite system. (C) 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
  • Lindqvist, Hannakaisa; Martikainen, Julia; Räbinä, Jukka; Penttilä, Antti; Muinonen, Karri (2018)
    Light scattering by particles large compared to the wavelength of incident light is traditionally solved using ray optics which considers absorption inside the particle approximately, along the ray paths. To study the effects rising from this simplification, we have updated the ray-optics code SIRIS to take into account the propagation of light as inhomogeneous plane waves inside an absorbing particle. We investigate the impact of this correction on traditional ray-optics computations in the example case of light scattering by ice crystals through the extended near-infrared (NIR) wavelength regime. In this spectral range, ice changes from nearly transparent to opaque, and therefore provides an interesting test case with direct connection and applicability to atmospheric remote-sensing measurements at NIR wavelengths. We find that the correction for inhomogeneous waves systematically increases the single-scattering albedo throughout the NIR spectrum for both randomly-oriented, column-like hexagonal crystals and ice crystals shaped like Gaussian random spheres. The largest increase in the single-scattering albedo is 0.042 for hexagonal crystals and 0.044 for Gaussian random spheres, both at λ=2.725 µm. Although the effects on the 4  ×  4 scattering-matrix elements are generally small, the largest differences are seen at 2.0 µm and 3.969 µm wavelengths where the correction for inhomogeneous waves affects mostly the backscattering hemisphere of the depolarization-connected P22/P11, P33/P11, and P44/P11. We evaluated the correction for inhomogeneous waves through comparisons against the discrete exterior calculus (DEC) method. We computed scattering by hexagonal ice crystals using the DEC, a traditional ray-optics code (SIRIS3), and a ray-optics code with inhomogeneous waves (SIRIS4). Comparisons of the scattering-matrix elements from SIRIS3 and SIRIS4 against those from the DEC suggest that consideration of the inhomogeneous waves brings the ray-optics solution generally closer to the exact result and, therefore, should be taken into account in scattering by absorbing particles large compared to the wavelength of incident light.