Formula for the calculation of integral cross sections in a Fourier expansion method

1997 ◽  
Vol 55 (1) ◽  
pp. 812-814 ◽  
Author(s):  
Zhifan Chen ◽  
Alfred Z. Msezane
Keyword(s):  
Cross Sections ◽  
Fourier Expansion ◽  
Expansion Method

Electron Scattering in Solids

1990 ◽  
Vol 48 (2) ◽  
pp. 4-5
Author(s):  
Ryuichi Shimizu ◽  
Ze-Jun Ding
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Angular Distribution ◽  
Elastic Scattering ◽  
Electron Scattering ◽  
Cross Sections ◽  
Expansion Method ◽  
Electron Excitation ◽  
Partial Wave Expansion ◽  
Backscattered Electrons

Monte Carlo simulation has been becoming most powerful tool to describe the electron scattering in solids, leading to more comprehensive understanding of the complicated mechanism of generation of various types of signals for microbeam analysis.The present paper proposes a practical model for the Monte Carlo simulation of scattering processes of a penetrating electron and the generation of the slow secondaries in solids. The model is based on the combined use of Gryzinski’s inner-shell electron excitation function and the dielectric function for taking into account the valence electron contribution in inelastic scattering processes, while the cross-sections derived by partial wave expansion method are used for describing elastic scattering processes. An improvement of the use of this elastic scattering cross-section can be seen in the success to describe the anisotropy of angular distribution of elastically backscattered electrons from Au in low energy region, shown in Fig.l. Fig.l(a) shows the elastic cross-sections of 600 eV electron for single Au-atom, clearly indicating that the angular distribution is no more smooth as expected from Rutherford scattering formula, but has the socalled lobes appearing at the large scattering angle.

Analytic solutions of the scattering by two multilayered dielectric spheres

1992 ◽  
Vol 70 (9) ◽  
pp. 696-705 ◽  
Author(s):  
A-K. Hamid ◽  
I. R. Ciric ◽  
M. Hamid
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Plane Electromagnetic Wave ◽  
Expansion Method ◽  
Analytic Solutions ◽  
Addition Theorem ◽  
Modal Expansion ◽  
Modal Expansion Method ◽  
Dielectric Spheres ◽  
Scattered Fields

The problem of plane electromagnetic wave scattering by two concentrically layered dielectric spheres is investigated analytically using the modal expansion method. Two different solutions to this problem are obtained. In the first solution the boundary conditions are satisfied simultaneously at all spherical interfaces, while in the second solution an iterative approach is used and the boundary conditions are satisfied successively for each iteration. To impose the boundary conditions at the outer surface of the spheres, the translation addition theorem of the spherical vector wave functions is employed to express the scattered fields by one sphere in the coordiante system of the other sphere. Numerical results for the bistatic and back-scattering cross sections are presented graphically for various sphere sizes, layer thicknesses and permittivities, and angles of incidence.

Chaotic mixing by oscillating a Stokeslet in a circular Hele-Shaw microfluidic device

2016 ◽  
Vol 5 (1) ◽  
pp. 1-8
Author(s):  
Yasser Aboelkassem
Keyword(s):  
Mathematical Modeling ◽  
Stream Function ◽  
Microfluidic Device ◽  
Fourier Expansion ◽  
Expansion Method ◽  
Small Oscillation ◽  
Chaotic Mixing ◽  
Mixing Efficiency ◽  
Induced Flow ◽  
Mixing Patterns

AbstractChaotic mixing by oscillating a Stokeslet in a circular Hele-Shaw microffluidic device is presented in this article. Mathematical modeling for the induced flow motions by moving a Stokeslet along the x-axis is derived using Fourier expansion method. The solution is formulated in terms of the velocity stream function. The model is then used to explore different stirring dynamics as function of the Stokeslet parameters. For instance, the effects of using various oscillation amplitudes and force strengths are investigated. Mixing patterns using Poincaré maps are obtained numerically and have been used to characterize the mixing efficiency. Results have shown that, for a given Stokeslet’s strength, efficient mixing can be obtained when small oscillation amplitudes are used. The present mixing platform is expected to be useful for many of biomicrofluidic applications.

Development of Three-Dimensional Neutron Kinetics Code Based on High Order Nodal Expansion Method in Hexagonal-Z Geometry

2018 ◽  
Author(s):  
Guo Chao ◽  
Liu Yu ◽  
He Hangxing ◽  
Liu Luguo ◽  
Wang Xiaoyu ◽  
...  
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Expansion Method ◽  
High Order ◽  
Benchmark Problems ◽  
Weighting Method ◽  
Control Rod ◽  
Order Polynomial ◽  
Runge Kutta ◽  
Nodal Expansion Method

To solve three-dimensional kinetics problems, a high order nodal expansion method for hexagonal-z geometry (HONEM) and a Runge-Kutta (RK) method are respectively adopted to deal with the spatial and temporal problem. In the HONEM, 1D partially-integrated flux are approximated by using four order polynomial. The two order polynomial is adopted to the approximation of partially-integrated leakages. The Runge-Kutta method is adopted as a tool for dispersing the time term of 3D kinetics equation. A flux weighting method (FWM) is used for obtaining homogenized cross sections of mix node. The three-dimensional hexagonal kinetics code has been developed based on this method and tested with two benchmark problems of VVER which are the control rod ejection without any feedback and with simple adiabatic Doppler feedback. The results calculated by this code agree well with the reference results and the code is validated.

A QUASICLASSICAL TRAJECTORY STUDY OF REACTIVE SCATTERING ON AN ANALYTICAL POTENTIAL ENERGY SURFACE FOR GeH2 SYSTEM

2011 ◽  
Vol 10 (02) ◽  
pp. 147-163
Author(s):  
LI ZHANG ◽  
CHAO-YONG ZHU ◽  
GANG JIANG ◽  
CHAOYUAN ZHU ◽  
Z. H. ZHU
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Cross Section ◽  
Cross Sections ◽  
Collision Energy ◽  
Energy Surface ◽  
Life Time ◽  
Expansion Method ◽  
Reverse Reaction ◽  
Analytical Potential

A quasiclassical trajectory method was employed to study reaction Ge+H 2 (v=0, j=0) and reverse reaction H+GeH (v=0, j=0) on an analytical potential energy surface obtained from simplified many-body expansion method with fitting to B3P86/CC-pVTZ calculations around a global minimum and a long-range van de Waals well plus spectroscopy data for diatomic molecules GeH and H2 . Reaction probabilities from both reaction and reverse reaction were calculated. Dominant reaction is complex-forming reaction Ge+H2 (v=0, j=0) → GeH2 , and its cross section is 10 times bigger than that of complex-forming reaction from the reverse reaction. There is no threshold effect for complex-forming reaction and the cross sections for both complex-forming reactions decrease with the increase of collision energy. Life time of complex is shown to be decreasing with increase of collision energy. Dominant reverse reaction is reaction H + GeH (v=0,j=0) → Ge+H2 ; the reaction probability decreases with the increase of collision energy and differential cross section shows that this reverse reaction has almost equal angular distribution at low collision energy and mostly forward scattering at high collision energy.

Dispersion study of plane-strain vibrations in poroelastic solid bars with polygonal cross-section

2016 ◽  
Vol 22 (1) ◽  
pp. 38-52 ◽  
Author(s):  
Sandhya Rani Bandari ◽  
Malla Reddy Perati ◽  
Gangadhar Reddy Gangu
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Plane Strain ◽  
Cross Section ◽  
Cross Sections ◽  
Fourier Expansion ◽  
Data Phase ◽  
Base Curve ◽  
Symmetric And Antisymmetric Modes ◽  
Relevant Material

This paper studies wave propagation in a poroelastic solid bar with polygonal cross-section under plane-strain conditions. The boundary conditions on the surface of the cylinder whose base curve is polygon are satisfied by means of the Fourier expansion collocation method. The frequency equations are discussed for both symmetric and antisymmetric modes in the framework of Biot’s theory of poroelastic solids. For illustration purposes, sandstone saturated materials and bony material are considered. The numerical results were computed as the basis of relevant material data . Phase velocity is computed against the wavenumber for various cross-sections and results are presented graphically.

scholarly journals Characteristics of porous beds based on fractal parameters

2017 ◽  
Vol 2 (20) ◽  
pp. 171-179
Author(s):  
Mirosław Bramowicz ◽  
Sławomir Kulesza ◽  
Wojciech Sobieski
Keyword(s):  
Fractal Dimension ◽  
Structure Function ◽  
Cross Sections ◽  
Fractal Analysis ◽  
Expansion Method ◽  
Mineral Deposit ◽  
Corner Frequency ◽  
Mineral Deposits ◽  
Fractal Parameters ◽  
Spatial System

The paper presents the results of a fractal analysis of the cross-sections of a porous mineral deposit consisting of spherical elements which formed a spatial system with varying porosity (0.4 to 0.95). The virtual deposit was generated using the Discrete Element Method in the YADE code by means of the so-called Radius Expansion Method. The fractal analysis was carried out using the structure function method, determining the fractal dimension (D), the topothesy (L) and the corner frequency (l) (MAINSAH et al. 2001). The conducted simulations have confirmed to a considerable extent the test results available in the literature involving the fractal analysis of mineral deposits with varying porosity. They clearly indicate that the fractal dimension does not change along with the porosity of the deposit, if the autocorrelation function or their transformations (e.g. structure function) methods are used. Moreover, based on the information available in the literature, it can be concluded that the value of the fractal dimension corresponds to mineral deposits with the specified geometric shapes of the elements which form them.

An Analysis of an Optical Fiber with Two Inhomogeneous Sector Holes by Circular Fourier Expansion Method

2008 ◽  
Vol E91-C (1) ◽  
pp. 41-47
Author(s):  
S. FURUKAWA ◽  
W. SATOU ◽  
T. HINATA ◽  
N. SHIMIZU
Keyword(s):  
Optical Fiber ◽  
Fourier Expansion ◽  
Expansion Method
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