Approximation of quasilayered medium and equations of imbedding in a three-dimensional wave propagation problem

1989 ◽  
Vol 32 (4) ◽  
pp. 352-360
Author(s):  
A. G. Bugrov
Keyword(s):  
Wave Propagation ◽  
Three Dimensional ◽  
Propagation Problem ◽  
Wave Propagation Problem ◽  
Dimensional Wave

Wave Diffraction Around Three-Dimensional Bodies in a Current

1996 ◽  
Vol 118 (4) ◽  
pp. 247-252 ◽  
Author(s):  
K. F. Cheung ◽  
M. Isaacson ◽  
J. W. Lee
Keyword(s):  
Wave Propagation ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Rigid Wall ◽  
Propagation Problem ◽  
Wave Forces ◽  
Linear Wave ◽  
Wave Propagation Problem ◽  
Linear Wave Propagation ◽  
A Current

The effects of a collinear current on the diffraction of regular waves around three-dimensional surface-piercing bodies are examined. With the current speed assumed to be small, the boundary-value problem is separated into a steady current problem with a rigid wall condition applied at the still water level and a linear wave propagation problem in the resulting current field. The boundary conditions of the wave propagation problem are satisfied by a time-stepping procedure and the field solution is obtained by an integral equation method. Free surface profiles, runup, and wave forces are described for a vertical circular cylinder in combined waves and a current. The current is shown to affect significantly the steady drift force and runup predictions. Comparisons of the computed wave forces are made with a previous numerical solution involving a semi-immersed sphere in deep water, and indicate good agreement.

IS WAVE PROPAGATION COMPUTABLE OR CAN WAVE COMPUTERS BEAT THE TURING MACHINE?

2002 ◽  
Vol 85 (2) ◽  
pp. 312-332 ◽  
Author(s):  
KLAUS WEIHRAUCH ◽  
NING ZHONG
Keyword(s):  
Wave Propagation ◽  
Turing Machine ◽  
Sobolev Spaces ◽  
Three Dimensional ◽  
Subject Classification ◽  
Physical Machine ◽  
The Church ◽  
Dimensional Wave

According to the Church-Turing Thesis a number function is computable by the mathematically defined Turing machine if and only if it is computable by a physical machine. In 1983 Pour-El and Richards defined a three-dimensional wave $u(t,x)$ such that the amplitude $u(0,x)$ at time 0 is computable and the amplitude $u(1,x)$ at time 1 is continuous but not computable. Therefore, there might be some kind of wave computer beating the Turing machine. By applying the framework of Type 2 Theory of Effectivity (TTE), in this paper we analyze computability of wave propagation. In particular, we prove that the wave propagator is computable on continuously differentiable waves, where one derivative is lost, and on waves from Sobolev spaces. Finally, we explain why the Pour-El-Richards result probably does not help to design a wave computer which beats the Turing machine.2000 Mathematical Subject Classification: 03D80, 03F60, 35L05, 68Q05.

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