Optical Cross-Sections of Soot Agglomerates: The model of the virtual refractive index and first-order multiple scattering

1996 ◽  
Vol 13 (2) ◽  
pp. 97-103 ◽  
Author(s):  
Rolf Dittmann
Author(s):  
S. Golladay

The theory of multiple scattering has been worked out by Groves and comparisons have been made between predicted and observed signals for thick specimens observed in a STEM under conditions where phase contrast effects are unimportant. Independent measurements of the collection efficiencies of the two STEM detectors, calculations of the ratio σe/σi = R, where σe, σi are the total cross sections for elastic and inelastic scattering respectively, and a model of the unknown mass distribution are needed for these comparisons. In this paper an extension of this work will be described which allows the determination of the required efficiencies, R, and the unknown mass distribution from the data without additional measurements or models. Essential to the analysis is the fact that in a STEM two or more signal measurements can be made simultaneously at each image point.


2020 ◽  
Author(s):  
Quanfu He ◽  
Zheng Fang ◽  
Ofir Shoshamin ◽  
Steven S. Brown ◽  
Yinon Rudich

Abstract. Accurate Rayleigh scattering and absorption cross-sections of atmospheric gases are essential for understanding the propagation of electromagnetic radiation in planetary atmospheres. Accurate extinction cross-sections are also essential for calibrating high finesse optical cavities and differential optical absorption spectroscopy and for accurate remote sensing. In this study, we measured the scattering and absorption cross-sections of carbon dioxide, nitrous oxide, sulfur hexafluoride, oxygen, and methane in the continuous wavelength range of 307–725 nm using Broadband Cavity Enhanced Spectroscopy (BBCES). The experimentally derived Rayleigh scattering cross-sections for CO2, N2O, SF6, O2, and CH4 agree with refractive index-based calculations, with a difference of 1.5 % and 1.1 %, 1.5 %, 2.9 %, and 1.4 % on average, respectively. The O2-O2 collision-induced absorption and absorption by methane are obtained with high precision at the 0.8 nm resolution of our BBCES instrument in the 307–725 nm wavelength range. New dispersion relations for N2O, SF6, and CH4 were derived using data in the UV-vis wavelength range. This study provides improved refractive index dispersion relations, n-based Rayleigh scattering cross-sections, and absorption cross-sections for these gases.


2020 ◽  
Author(s):  
T. Lewiński ◽  
S. Czarnecki

Abstract By endowing El Fatmi’s theories of bars with first-order warping functions due to torsion and shear, a family of theories of bars, of various applicability ranges, is effectively constructed. The theories thus formed concern bars of arbitrary cross-sections; they are reformulations of the mentioned theories by El Fatmi and theories by Kim and Kim, Librescu and Song, Vlasov and Timoshenko. The Vlasov-like theory thus developed is capable of describing the torsional buckling and lateral buckling phenomena of bars of both solid and thin-walled cross-sections, which reflects the non-trivial correspondence, noted by Wagner and Gruttmann, between the torsional St.Venant’s warping function and the contour-wise defined warping functions proposed by Vlasov. Moreover, the present paper delivers an explicit construction of the constitutive equations of Timoshenko’s theory; the equations linking transverse forces with the measures of transverse shear turn out to be coupled for all bars of asymmetric cross-sections. The modeling is hierarchical: the warping functions are numerically constructed by solving the three underlying 2D scalar elliptic problems, providing the effective characteristics for the 1D models of bars. The 2D and 1D problems are indissolubly bonded, thus forming a unified scientific tool, deeply rooted in the hitherto existing knowledge on elasticity of elastic straight bars.


2010 ◽  
Vol 19 (10) ◽  
pp. 1947-1960
Author(s):  
YONG JOO KIM ◽  
JONG-KWAN WOO ◽  
MOON HOE CHA

We present analytic expressions for the zero-order eikonal phase shift and its first-order correction by approximating a distance between two colliding nuclei. This formalism has been applied to elastic scatterings of the 12 C + 40 Ca and the 12 C + 90 Zr systems at E lab = 420 MeV , and the 16 O + 40 Ca and the 16 O + 90 Zr ones at E lab = 1503 MeV . The calculated angular distributions, taking into account up to the analytic first-order eikonal phase shift, are found to be in fairly good agreement with the observed data. The reaction cross-sections obtained from the present model produce very excellent agreements with ones of exact first-order eikonal model calculations. We have found that analytic eikonal phase shift including the first-order correction is one theoretical method to the analysis of heavy-ion elastic scattering.


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