Calculation of reflection and transmission coefficients for a class of one‐dimensional wave propagation problems in inhomogeneous media

1973 ◽  
Vol 14 (7) ◽  
pp. 963-972 ◽  
Author(s):  
Alfredo Baños
Keyword(s):  
Wave Propagation ◽  
Inhomogeneous Media ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Dimensional Wave

Generalization of von Neumann analysis for a model of two discrete half-spaces: The acoustic case

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM35-SM46 ◽  
Author(s):  
Matthew M. Haney
Keyword(s):  
Wave Propagation ◽  
Numerical Model ◽  
Finite Difference ◽  
Stability Criterion ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Von Neumann ◽  
Transmission Coefficients ◽  
Strong Material ◽  
Von Neumann Analysis

Evaluating the performance of finite-difference algorithms typically uses a technique known as von Neumann analysis. For a given algorithm, application of the technique yields both a dispersion relation valid for the discrete time-space grid and a mathematical condition for stability. In practice, a major shortcoming of conventional von Neumann analysis is that it can be applied only to an idealized numerical model — that of an infinite, homogeneous whole space. Experience has shown that numerical instabilities often arise in finite-difference simulations of wave propagation at interfaces with strong material contrasts. These interface instabilities occur even though the conventional von Neumann stability criterion may be satisfied at each point of the numerical model. To address this issue, I generalize von Neumann analysis for a model of two half-spaces. I perform the analysis for the case of acoustic wave propagation using a standard staggered-grid finite-difference numerical scheme. By deriving expressions for the discrete reflection and transmission coefficients, I study under what conditions the discrete reflection and transmission coefficients become unbounded. I find that instabilities encountered in numerical modeling near interfaces with strong material contrasts are linked to these cases and develop a modified stability criterion that takes into account the resulting instabilities. I test and verify the stability criterion by executing a finite-difference algorithm under conditions predicted to be stable and unstable.

scholarly journals Generalized Continuity Equation for Quasi-Hermitian Hamiltonians

10.14311/1803 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Amine B. Hammou
Keyword(s):  
Continuity Equation ◽  
Delta Function ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Generalized Continuity ◽  
Unitarity Relation ◽  
Function Potential

The continuity relation is generalized to quasi-Hermitian one-dimensional Hamiltonians. As an application we show that the reflection and transmission coefficients computed with the generalized current obey the conventional unitarity relation for the continuous double delta function potential.

scholarly journals Wave propagation in a non-uniform string

2011 ◽  
Vol 33 (4) ◽  
pp. 4306-4306
Author(s):  
Fernando Fuzinatto Dall'Agnol
Keyword(s):  
Wave Propagation ◽  
Pulse Width ◽  
Mass Density ◽  
Reflection And Transmission Coefficients ◽  
Antireflection Coatings ◽  
Reflection And Transmission ◽  
Physical Systems ◽  
Transmission Coefficients

In this article I present the behavior of the reflection and transmission coefficients of a pulse at a joint between two strings with mass densities μ1and μ2. The joint is made of a string segment with mass density varying linearly from μ1 to μ2. It will be shown that the reflection of the pulse at the joint depends largely on the ratio between the pulse width and the length of the joint. Analogies with other physical systems such as antireflection coatings and tsunamis will be considered briefly.

scholarly journals Quantum Mechanical Reflection and Transmission Coefficients for a Particle through a OneDimensional Vertical Step Potential

2019 ◽  
Vol 8 (11) ◽  
pp. 2882-2886
Keyword(s):  
Laplace Transformation ◽  
Reflection And Transmission Coefficients ◽  
Quantum Mechanical ◽  
Mathematical Tool ◽  
Science And Engineering ◽  
Step Potential ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Vertical Step

In this paper, we illustrate an application of the Laplace transformation for finding the quantum mechanical Reflection and Transmission coefficients for a particle through a one-dimensional vertical step potential. Quantum mechanics is one of the branches of physics in which the physical problems are solved by algebraic and analytic methods. By applying the Laplace transformation, we can find the quantum mechanical Reflection and Transmission coefficients for a particle through a one-dimensional vertical step potential. Generally, the Laplace transformation has been applied in different areas of science and engineering and makes it easier to solve the problems inengineering applications. It is a mathematical tool which has been put to use for solving the differential equations without finding their general solutions. It has applications in nearly all science and engineering disciplines like analysis of electrical circuits, heat and mass transfer, fluid dynamics, nuclear physics, process controls, quantum mechanical problems,etc.

Evaluation of Moisture Content in Concrete with Microwave

2006 ◽  
Vol 312 ◽  
pp. 311-318 ◽  
Author(s):  
Xiao Ming Wang ◽  
Yinghao Teo ◽  
Wing K. Chiu ◽  
Greg Foliente
Keyword(s):  
Moisture Content ◽  
Water Content ◽  
Condition Monitoring ◽  
Reflection And Transmission Coefficients ◽  
Physical Change ◽  
Microwave Propagation ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Permittivity And Permeability

Generally, any chemical or physical change in a material may cause variation in its permittivity and permeability. The propagation of microwave through the material can be affected by these variation in properties. The analysis of microwave propagation through materials may therefore provide a means for condition monitoring. This paper utilizes a one-dimensional scenario, demonstrating the feasibility to link measurable reflection and transmission coefficients of microwave to concrete permittivity and permeability, which are essentially associated with water content in concrete. As a result, water content can then be monitored through the measurement of these coefficients. The study also demonstrates the feasibility of using the same technique to estimate the thickness of the concrete that microwave propagates through.

Reflection and transmission coefficients for seismic waves in ellipsoidally anisotropic media

Geophysics ◽  
1979 ◽  
Vol 44 (1) ◽  
pp. 27-38 ◽  
Author(s):  
P. F. Daley ◽  
F. Hron
Keyword(s):  
Wave Propagation ◽  
Anisotropic Medium ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Earth ◽  
Special Case

The deficiency of an isotropic model of the earth in the explanation of observed traveltime phenomena has led to the mathematical investigation of elastic wave propagation in anisotropic media. A type of anisotropy dealt with in the literature (Potsma, 1955; Cerveny and Psencik, 1972; and Vlaar, 1968) is uniaxial anisotropy or transverse isotropy. A special case of transverse isotropy which assumes the wavefronts to be ellipsoids of revolution has been used by Cholet and Richard (1954) and Richards (1960) in accounting for the observed traveltimes at Berraine in the Sahara and in the foothills of Western Canada. The kinematics of this problem have been treated in a number of papers, the most notable being Gassmann (1964). However, to appreciate fully the effect of anisotropy, the dynamics of the problem must be explored. Assuming a model of the earth consisting of plane transversely isotropic layers with the axes of anisotropy perpendicular to the interfaces, a prime requisite for obtaining amplitude distance curves or synthetic seismograms is the calculation of reflection and transmission coefficients at the interfaces. In this paper the special case of ellipsoidal anisotropy will be considered. That the quasi‐shear SV wavefront is forced to be spherical by this assumption is unfortunate, but it is instructive to investigate this simple anisotropic model as it incorporates many features inherent to wave propagation in a more general anisotropic medium. A brief outline of the theory for wave propagation in an ellipsoidally anisotropic medium is given and the analytic expressions for the reflection and transmission coefficients are listed. A complete derivation of reflection and transmission coefficients in transversely isotropic media can be found in Daley and Hron (1977). Finally, all 24 possible reflection and transmission coefficients and surface conversion coefficients are displayed for varying degrees of anisotropy.

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