scholarly journals On the scattering of waves by nearly hard or soft incomplete vertical barriers in water of infinite depth

1998 ◽  
Vol 39 (3) ◽  
pp. 293-307
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Perturbation Theory ◽  
Infinite Depth ◽  
Hard Limit ◽  
Vertical Barriers ◽  
Progressive Waves ◽  
Porous Barriers

AbstractIn this paper the scattered progressive waves are determined due to progressive waves incident normally on certain types of partially immersed and completely submerged vertical porous barriers in water of infinite depth. The forms are approximate only, and are obtained using perturbation theory for nearly hard or soft barriers having high and low porosities respectively. The results for arbitrary porosity are difficult to obtain, in contrast to the well known hard limit of impermeable barriers.

The effect of surface tension on the progressive waves due to incomplete vertical wave-makers in water of infinite depth

1991 ◽  
Vol 435 (1894) ◽  
pp. 293-319 ◽  
Keyword(s):  
Surface Tension ◽  
Reduction Method ◽  
Edge Condition ◽  
Infinite Depth ◽  
Transmitted Waves ◽  
Time Harmonic ◽  
Vertical Barriers ◽  
Wave Maker ◽  
Progressive Waves ◽  
Effect Of Surface

In this paper the influence of surface tension is allowed for in deriving formulas that determine the velocity potentials describing the outgoing progressive waves for two-dimensional time-harmonic motion due to both partially immersed and completely submerged vertical wave-makers in water of infinite depth. For this purpose an effective reduction method is developed to extend a known method suitable only in the absence of surface tension. The two results are used to find the reflected and transmitted waves due to waves incident upon partially immersed and completely submerged fixed vertical barriers, after reformulation as wave-maker problems; and to find the outgoing waves due to a partially immersed vertical hinged plate as a standard example. Certain edge-slope constants needed for the partially immersed wave-maker problem are evaluated using an appropriate dynamical edge condition.

scholarly journals On wave motion in a two-layered liquid of infinite depth in the presence of surface and interfacial tension

1994 ◽  
Vol 35 (3) ◽  
pp. 302-322 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Free Surface ◽  
Interfacial Tension ◽  
Vertical Wall ◽  
Small Time ◽  
Underlying Assumption ◽  
Wave Source ◽  
Infinite Depth ◽  
Surface And Interface ◽  
All Solutions ◽  
Progressive Waves

AbstractIn this paper various two-dimensional motions are determined for waves in a stratified region of infinite total depth with a free surface containing two superposed liquids, allowing for the effects of surface and interfacial tension. The fundamental set of wave-source potentials for the two layers is used to construct the set of slope potentials that produce discontinuous free-surface and interface slopes. The latter potentials are then utilized to obtain the potentials for waves due to both heaving vertical plates and incident progressive waves against a vertical wall. The underlying assumption of small time-harmonic motion pertains, described by a pair of velocity potentials for the two layers satisfying coupled linearized boundary-value problems, and all solutions are obtained in terms of their matching basic solutions. The technique for applying Green's theorem in the two layers is developed for use with the wave-source potentials, which themselves are found to obey a generalised reciprocity principle. Familiar results for a single liquid of infinite depth are hereby extended, but the new feature emerges of there being two types of progressive waves in all solutions. For ease of presentation the solutions are obtained for a particular relationship between surface and interfacial tension.

Complementary approximations to wave scattering by vertical barriers

1995 ◽  
Vol 294 ◽  
pp. 155-180 ◽  
Author(s):  
R. Porter ◽  
D. V. Evans
Keyword(s):  
Wave Scattering ◽  
Galerkin Approximation ◽  
Finite Depth ◽  
Accurate Method ◽  
Scattering Problems ◽  
Relative Ease ◽  
Infinite Depth ◽  
Vertical Barrier ◽  
Vertical Barriers ◽  
Depth Water

Scattering of waves by vertical barriers in infinite-depth water has received much attention due to the ability to solve many of these problems exactly. However, the same problems in finite depth require the use of approximation methods. In this paper we present an accurate method of solving these problems based on a Galerkin approximation. We will show how highly accurate complementary bounds can be computed with relative ease for many scattering problems involving vertical barriers in finite depth and also for a sloshing problem involving a vertical barrier in a rectangular tank.

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

Energy, Information, and Superluminal Speed in Quantum Electrodynamics

2020 ◽  
pp. 27-33
Author(s):  
Boris A. Veklenko
Keyword(s):  
Electromagnetic Field ◽  
Perturbation Theory ◽  
Quantum Electrodynamics ◽  
Excited Atom ◽  
Standard Quantum ◽  
Energy Information

Without using the perturbation theory, the article demonstrates a possibility of superluminal information-carrying signals in standard quantum electrodynamics using the example of scattering of quantum electromagnetic field by an excited atom.

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