Exact and Glauber amplitudes in multi-channel scattering

1979 ◽  
Vol 57 (11) ◽  
pp. 1952-1958 ◽  
Author(s):  
W. van Dijk ◽  
M. Razavy
Keyword(s):  
Composite System ◽  
Numerical Solutions ◽  
Particle System ◽  
Reflection Coefficients ◽  
One Dimensional ◽  
First Order ◽  
Transmission Coefficients ◽  
Transmission And Reflection Coefficients ◽  
Invariant Embedding ◽  
Transmission And Reflection

A model for one-dimensional many-channel scattering of a particle from a composite system is considered. It is assumed that the target cannot break up. Using Bellman's method of invariant embedding, a system of non-linear first-order differential equations with one-point boundary conditions is obtained for the transmission and reflection coefficients. These equations have stable numerical solutions. An alternative invariant embedding with the approximation of no reflection at any stage of the scattering process yields the Glauber approximation for the transmission coefficients. These formulations are used to compare the exact and the Glauber amplitudes for a projectile scattering from a bound two-particle system. It is found that unlike the inelastic Glauber amplitudes, the elastic Glauber amplitudes are very good approximations to the exact results.

Transmission and Reflection Coefficients for Damage Identification in 1D Elements

2009 ◽  
Vol 413-414 ◽  
pp. 95-100 ◽  
Author(s):  
Marek Krawczuk ◽  
Magdalena Palacz ◽  
Arkadiusz Zak ◽  
Wiesław M. Ostachowicz
Keyword(s):  
Damage Identification ◽  
Reflection And Transmission Coefficients ◽  
Reflection Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Transmission And Reflection Coefficients ◽  
Structural Discontinuity ◽  
Spectral Finite Element ◽  
Processing Techniques ◽  
Transmission And Reflection

According to the latest research results presented in the literature changes in propagating waves are one of the most promising parameters for damage identification algorithms. Numerous publications describe methods of damage identification based on the analysis of signals reflected from damage. They also include complicated signal processing techniques. Such methods work well for damage localisation, but it is rather difficult to use them in order to estimate the size of damage. It is natural that propagating wave reflects from any structural discontinuity. The bigger the disturbance the bigger part of a propagating wave reflects from it. The amount of energy reflected and transmitted through any discontinuity can expressed as reflection and transmission coefficients. In the literature different application for these coefficients may be found – the most often cited application is connected with localising changes in the geometry of structures. Changes in the coefficients due to cross section variations in rods and beams or due to existence of stiffeners in plates are well documented. However there are no application of using the reflection and transmission coefficients for damage size identification. For this reason the analysis presented in this paper has been carried out. The article presents a method of damage identification in 1D elements based on the wave propagation phenomenon and changes in reflection and transmission coefficients. The changes in transmission and reflection coefficients for waves propagating in isotropic rods with different types of damage have been analysed. The rods have been modelled with the elementary, two and three mode theories or rods. For numerical modelling the Spectral Finite Element Method has been used. Several examples are given in the paper.

19.—Propagation of Weak Discontinuities in a Layered Hyperelastic Half-space

1976 ◽  
Vol 75 (3) ◽  
pp. 209-221 ◽  
Author(s):  
Erdogan S. Suhubi ◽  
Alan Jeffrey
Keyword(s):  
Half Space ◽  
Reflection Coefficients ◽  
Initial Condition ◽  
One Dimensional ◽  
Transmission And Reflection Coefficients ◽  
Weak Discontinuities ◽  
Acceleration Waves ◽  
The One ◽  
The Waves ◽  
Transmission And Reflection

SYNOPSISThis paper investigates the one-dimensional propagation of weak discontinuities, that is acceleration waves, in a homogeneous and isotropic half-space composed of an arbitrary number of non-linearly hyperelastic layers. The transmission and reflection coefficients are evaluated in terms of the initial condition at the boundary, and the steepening of the waves to form a shock is discussed. The results are specialised to the case of periodic layering.

scholarly journals Transmission, Reflection and Dissipation of Microwaves in Magnetic Composites with Nanocrystalline Finemet-Type Flakes

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3499
Author(s):  
Anatoly B. Rinkevich ◽  
Dmitry V. Perov ◽  
Yuriy I. Ryabkov
Keyword(s):  
Composite Material ◽  
Microwave Absorption ◽  
Nanocrystalline Alloy ◽  
Reflection Coefficients ◽  
Magnetic Composites ◽  
Transmission And Reflection Coefficients ◽  
Wave Interference ◽  
Microwave Losses ◽  
Frequency Dependences ◽  
Transmission And Reflection

The microwave properties of a composite material containing flakes of finemet-type nanocrystalline alloy placed in the epoxy matrix have been investigated. Two compositions have been studied: with 15% and 30% flakes. Frequency dependences of transmission and reflection coefficients are measured in the frequency range from 12 to 38 GHz. The dielectric permittivity and magnetic permeability are obtained, and the microwave losses are calculated. The dependences of transmission and reflection coefficients have been drawn as functions of wave frequency and thickness of the composite material, taking into account the frequency dependences of permittivity and permeability. The regions of maximal and minimal microwave absorption have been defined. The influence of wave interference on the frequency dependence of microwave absorption is studied.

DKP equation with smooth barrier

2021 ◽  
Author(s):  
O. Langueur ◽  
M. Merad ◽  
A. Rassoul
Keyword(s):  
Hypergeometric Function ◽  
Numerical Study ◽  
Confluent Hypergeometric Function ◽  
Reflection Coefficients ◽  
Step Potential ◽  
Dkp Equation ◽  
Transmission And Reflection Coefficients ◽  
Special Cases ◽  
Rectangular Barrier ◽  
Transmission And Reflection

In this paper, we study the Duffin–Kemmer–Petiau (DKP) equation in the presence of a smooth barrier in dimensions space–time (1+1) dimensions. The eigenfunctions are determined in terms of the confluent hypergeometric function [Formula: see text]. The transmission and reflection coefficients are calculated, special cases as a rectangular barrier and step potential are analyzed. A numerical study is presented for the transmission and reflection coefficients graphs for some values of the parameters [Formula: see text] are plotted.

Materials Evaluation and Environmental Monitoring Utilizing an Acoustic Resonance

2020 ◽  
Author(s):  
Hironori Tohmyoh
Keyword(s):  
Resonant Frequency ◽  
Environmental Monitoring ◽  
Water Film ◽  
Acoustic Resonance ◽  
Acoustic Properties ◽  
Reflection Coefficients ◽  
Plate Interface ◽  
Transmission And Reflection Coefficients ◽  
Transmission And Reflection ◽  
Outer Environment

Abstract This paper presents the materials evaluation and environmental monitoring techniques utilizing the acoustic resonance, which have been developed by the authors. When the ultrasound passes through thin layer, the transmission and reflection coefficients take their maximum and the minimum values at the resonant frequency. We call this acoustic resonance. The acoustic properties of a polymer film, e.g., the acoustic impedance, ultrasonic velocity, and density, can be determined by observing the acoustic resonance, which occurs at the water/film/reflection plate interface. Acoustic resonance occurs at the reflection plate/film/outer environment interface sensitively changes depending on the outer environment. With use of this, the temperature of the water as an outer environment is tried to be monitored.

scholarly journals Study of superradiance in the Lambert-W potential barrier

2019 ◽  
Vol 34 (16) ◽  
pp. 1950087 ◽  
Author(s):  
Luis Puente ◽  
Carlos Cocha ◽  
Clara Rojas
Keyword(s):  
Reflection Coefficient ◽  
Potential Barrier ◽  
Gordon Equation ◽  
Reflection Coefficients ◽  
Hyperbolic Tangent ◽  
Step Potential ◽  
Transmission And Reflection Coefficients ◽  
Klein Gordon ◽  
Klein Gordon Equation ◽  
Transmission And Reflection

We present a new potential barrier that presents the phenomenon of superradiance when the reflection coefficient [Formula: see text] is greater than one. We calculated the transmission and reflection coefficients for three different regions. The results are compared with those obtained for the hyperbolic tangent potential barrier and the step potential barrier. We also present the solution of the Klein–Gordon equation with the Lambert-[Formula: see text] potential barrier in terms of the Heun Confluent functions.

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