Theorems of Wiener and Lévy; the Wiener–Hopf method

2020 ◽  
pp. 283-295
Author(s):  
Richard Beals ◽  
Roderick S. C. Wong
Keyword(s):  
Hopf Method

SH-Wave Scattering From the Interface Defect

2017 ◽  
Vol 5 (1) ◽  
pp. 45-50
Author(s):  
Myron Voytko ◽  
◽  
Yaroslav Kulynych ◽  
Dozyslav Kuryliak
Keyword(s):  
Half Space ◽  
Wave Diffraction ◽  
Scattered Field ◽  
Wave Scattering ◽  
Elastic Layer ◽  
Analytical Form ◽  
Structure Parameters ◽  
Sh Wave ◽  
Interface Defect ◽  
Hopf Method

The problem of the elastic SH-wave diffraction from the semi-infinite interface defect in the rigid junction of the elastic layer and the half-space is solved. The defect is modeled by the impedance surface. The solution is obtained by the Wiener- Hopf method. The dependences of the scattered field on the structure parameters are presented in analytical form. Verifica¬tion of the obtained solution is presented.

scholarly journals Deep neural networks for waves assisted by the Wiener–Hopf method

2020 ◽  
Vol 476 (2235) ◽  
pp. 20190846 ◽  
Author(s):  
Xun Huang
Keyword(s):  
Neural Networks ◽  
Wave Equations ◽  
Deep Neural Networks ◽  
Research Strategy ◽  
Propagation Model ◽  
Physical Constraints ◽  
Aerospace Applications ◽  
Feed Forward Network ◽  
New Perspective ◽  
Hopf Method

In this work, the classical Wiener–Hopf method is incorporated into the emerging deep neural networks for the study of certain wave problems. The essential idea is to use the first-principle-based analytical method to efficiently produce a large volume of datasets that would supervise the learning of data-hungry deep neural networks, and to further explain the working mechanisms on underneath. To demonstrate such a combinational research strategy, a deep feed-forward network is first used to approximate the forward propagation model of a duct acoustic problem, which can find important aerospace applications in aeroengine noise tests. Next, a convolutional type U-net is developed to learn spatial derivatives in wave equations, which could help to promote computational paradigm in mathematical physics and engineering applications. A couple of extensions of the U-net architecture are proposed to further impose possible physical constraints. Finally, after giving the implementation details, the performance of the neural networks are studied by comparing with analytical solutions from the Wiener–Hopf method. Overall, the Wiener–Hopf method is used here from a totally new perspective and such a combinational research strategy shall represent the key achievement of this work.

Temperature Distribution in a Cylindrical Rod Moving From a Chamber at One Temperature to a Chamber at Another Temperature

1964 ◽  
Vol 86 (2) ◽  
pp. 265-270 ◽  
Author(s):  
G. Horvay ◽  
M. Dacosta
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Arbitrary Constant ◽  
Families Of Curves ◽  
Special Cases ◽  
Method Of Solution ◽  
Lower Chamber ◽  
Higher Temperature ◽  
Hopf Method ◽  
The Heat Transfer Coefficient

When an infinitely long cylindrical rod travels from a chamber at one temperature ϑa to a chamber (insulated from the first) at a higher temperature ϑf, then heat will leak out along the rod from the second chamber to the first, whose amount decreases as the speed of the rod increases. Using the Wiener-Hopf method of solution, we determine the temperature distribution in the rod for the case where in the second chamber the heat-transfer coefficient h+ is infinite, while in the first chamber it has an arbitrary constant value h. Families of curves illustrate the temperature distribution in the two special cases where h = ∞ (isothermal boundary conditions in lower chamber) and where h = 0 (rod is insulated in lower chamber).

Wiener-Hopf Method in Elastodynamics

1993 ◽  
pp. 220-255
Author(s):  
Vladimir B. Poruchikov
Keyword(s):  
Hopf Method

V.—Bifurcation of a Parallel-Plate Waveguide by a Unidirectionally Conducting Screen

1965 ◽  
Vol 67 (1) ◽  
pp. 50-68
Author(s):  
R. K. Arora
Keyword(s):  
Slow Wave ◽  
Parallel Plate ◽  
Transverse Electric ◽  
Transverse Magnetic ◽  
Hybrid Wave ◽  
Parallel Plate Waveguide ◽  
Hopf Method ◽  
Conducting Screen ◽  
Electric Mode ◽  
Transverse Electric Mode

SynopsisThe types of modes which may exist in an infinite parallel-plate waveguide with a centrally-placed unidirectionally conducting screen are studied. The effect of bifurcating an infinite parallel-plate waveguide by such a screen in the region x>O is investigated when a transverse electric mode is incident on the bifurcated region. The problem is solved by the Wiener-Hopf method, and expressions are derived for the amplitudes and phases of the reflected and transmitted modes. It is found that the transmitted field contains a hybrid wave and a slow wave, and the reflected field contains transverse electric and transverse magnetic waves.

The effect of a velocity-dependent charge-exchange kernel on neutral-atom transport in a half-space plasma: exact solution

1990 ◽  
Vol 44 (2) ◽  
pp. 285-302 ◽  
Author(s):  
A. K. Prinja ◽  
M. M. R. Williams
Keyword(s):  
Exact Solution ◽  
Half Space ◽  
Charge Exchange ◽  
Space Plasma ◽  
Total Charge ◽  
Angle Distribution ◽  
Velocity Dependence ◽  
Charge Exchange Reaction ◽  
Hopf Method ◽  
Exchange Kernel

A symmetric factorization of the velocity-dependent charge-exchange kernel (the so-called separable-kernel model) is used in the Boltzmann equation for neutral atoms to obtain an exact solution for a half-space plasma by the Wiener-Hopf method. This work generalizes earlier work employing constant, velocity-independent charge-exchange interactions to the case of an arbitrary velocity dependence of the Maxwellian averaged charge-exchange reaction rate. The effects of velocity dependence on the speed-angle distribution of escaping neutrals and the total charge-exchange rate in the half-space are shown to be significant. It is also shown how the Wiener-Hopf method can be applied to such problems with a realistic Maxwellian plasma background, without first approximating the ion distribution.

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