The fundamental solution for the axially symmetric wave equation

1977 ◽  
Vol 67 (1) ◽  
pp. 83-100 ◽  
Author(s):  
Albert E. Heins
Keyword(s):  
Wave Equation ◽  
Fundamental Solution ◽  
Axially Symmetric ◽  
Symmetric Wave

The fundamental solution for the axially symmetric wave equation II

1980 ◽  
Vol 87 (3) ◽  
pp. 515-521
Author(s):  
Albert E. Heins
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Equation ◽  
Fundamental Solution ◽  
Free Space ◽  
Axially Symmetric ◽  
Partial Differential ◽  
Symmetric Wave ◽  
Alternate Forms ◽  
Image Position

In a recent paper, hereafter referred to as I (1) we derived two alternate forms for the fundamental solution of the axially symmetric wave equation. We demonstrated that for α > 0, the fundamental solution (the so-called free space Green's function) of the partial differential equationcould be written asif b > rorif r > b.

scholarly journals Achromatic axially symmetric wave plate

2012 ◽  
Vol 20 (28) ◽  
pp. 29260 ◽  
Author(s):  
Toshitaka Wakayama ◽  
Kazuki Komaki ◽  
Yukitoshi Otani ◽  
Toru Yoshizawa
Keyword(s):  
Axially Symmetric ◽  
Wave Plate ◽  
Symmetric Wave

A Modulus for the 3-Dimensional Wave Equation With Noise: Dealing With a Singular Kernel

1993 ◽  
Vol 45 (6) ◽  
pp. 1263-1275
Author(s):  
C. Mueller
Keyword(s):  
Wave Equation ◽  
Fundamental Solution ◽  
Modulus Of Continuity ◽  
Gaussian Noise ◽  
Singular Kernel ◽  
3 Dimensional ◽  
Noise Term ◽  
Dimensional Wave

AbstractWe give a modulus of continuity for solutions of the wave equation with a noise term:utt = Δu + a(u) + b(u)G, x ∈ ℝ3where G is a Gaussian noise. This case is more difficult than in lower dimensions because the fundamental solution of the wave equation is singular.

MODEL AND APPLICATION OF IMPACT WAVE IN MEASURING THE DYNAMIC CHARACTERISTIC OF MICROSTRUCTURE

2005 ◽  
Vol 15 (02) ◽  
pp. 243-248
Author(s):  
YANPING BAI ◽  
JIANZHONG WANG ◽  
ZHEN JIN
Keyword(s):  
Wave Propagation ◽  
Dynamic Characteristic ◽  
Integral Transform ◽  
Experimental System ◽  
Theoretical Formula ◽  
Longitudinal Impact ◽  
Axially Symmetric ◽  
Theoretical Formulation ◽  
Impact Wave ◽  
Symmetric Wave

The model of transient axially symmetric wave propagation in a circular elastic bar is studied by using the elastic wave propagation theory and the methods of integral transform. The numerical results of the model of longitudinal impact wave velocity are shown using a method of numerical analysis. This theoretical formula and methods of analysis is used in an experimental system to measure the dynamic characteristic of microstructure. Curves of the wave peak emulation of Davies bar are obtained by using theoretical formulation.

scholarly journals Scalar resonances in axially symmetric spacetimes

2015 ◽  
Vol 24 (05) ◽  
pp. 1550037
Author(s):  
Ignacio F. Ranea-Sandoval ◽  
Héctor Vucetich
Keyword(s):  
Wave Equation ◽  
Scalar Wave ◽  
Axially Symmetric ◽  
Closed Timelike Curves ◽  
Scalar Wave Equation ◽  
Kerr Spacetime ◽  
Symmetric Spacetimes ◽  
Resonant Modes ◽  
Unstable Solutions ◽  
Scalar Resonances

We study properties of resonant solutions to the scalar wave equation in several axially symmetric spacetimes. We prove that nonaxial resonant modes do not exist neither in the Lanczos dust cylinder, the extreme (2 + 1) dimensional Bañados–Taitelboim–Zanelli (BTZ) spacetime nor in a class of simple rotating wormhole solutions. Moreover, we find unstable solutions to the wave equation in the Lanczos dust cylinder and in the r2 < 0 region of the extreme (2 + 1) dimensional BTZ spacetime, two solutions that possess closed timelike curves. Similarities with previous results obtained for the Kerr spacetime are explored.

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