Nondestructive Depth Profiling of a Diffuse Interface

1988 ◽  
Vol 142 ◽  
Author(s):  
Anthony N. Sinclair ◽  
Phineas Dickstein ◽  
Michael A. Graf
Keyword(s):  
Wave Equation ◽  
Reflection Coefficient ◽  
Theoretical Calculations ◽  
Homogeneous Medium ◽  
Depth Profiling ◽  
Diffuse Interface ◽  
One Dimensional ◽  
Frequency Comparison ◽  
The One ◽  
Dimensional Wave

AbstractA numerical solution of the one-dimensional wave equation is used to find the characteristics of wave propagation in a non-homogeneous medium. The solution is used to determine the magnitude and phase of the reflection coefficient at a diffuse interface. The result is found to be strongly dependent on sonic frequency. Comparison is made between theoretical calculations and measurements of the reflection coefficient at a copper-to-nickel diffusion bond.

Thermally corrected solutions of the one-dimensional wave equation for the laser-induced ultrasound

2021 ◽  
Vol 130 (2) ◽  
pp. 025104
Author(s):  
Misael Ruiz-Veloz ◽  
Geminiano Martínez-Ponce ◽  
Rafael I. Fernández-Ayala ◽  
Rigoberto Castro-Beltrán ◽  
Luis Polo-Parada ◽  
...  
Keyword(s):  
Wave Equation ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

scholarly journals Сlassical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition

2020 ◽  
Vol 64 (6) ◽  
pp. 657-662
Author(s):  
V. I. Korzyuk ◽  
J. V. Rudzko
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Mixed Problem ◽  
Method Of Characteristics ◽  
Smooth Boundary ◽  
Analytical Form ◽  
Initial Condition ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

In this article, we study the classical solution of the mixed problem in a quarter of a plane and a half-plane for a one-dimensional wave equation. On the bottom of the boundary, Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at one point. Smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. Uniqueness is proved and conditions are established under which a piecewise-smooth solution exists. The problem with linking conditions is considered.

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