Radiation and scattering from three-dimensional bodies of arbitrary shape determined by an FMM-POM hybrid formulation

1996 ◽  
Author(s):  
James A. Anderson ◽  
Adrian S. King
Keyword(s):  
Arbitrary Shape ◽  
Three Dimensional ◽  
Hybrid Formulation

scholarly journals Hybrid Formulation of Three-dimensional Limit Analysis

2011 ◽  
Vol 67 (2) ◽  
pp. I_241-I_250
Author(s):  
Shunsuke MIKI ◽  
Jun SAITO ◽  
Shun-ichi KOBAYASHI
Keyword(s):  
Limit Analysis ◽  
Three Dimensional ◽  
Hybrid Formulation

Stability of flow in a channel with longitudinal grooves

2014 ◽  
Vol 757 ◽  
pp. 613-648 ◽  
Author(s):  
H. V. Moradi ◽  
J. M. Floryan
Keyword(s):  
Reynolds Number ◽  
Small Amplitude ◽  
Arbitrary Shape ◽  
Critical Reynolds Number ◽  
Critical Role ◽  
Three Dimensional ◽  
Travelling Wave ◽  
Two Dimensional ◽  
Wave Instability ◽  
Long Wavelength

AbstractThe travelling wave instability in a channel with small-amplitude longitudinal grooves of arbitrary shape has been studied. The disturbance velocity field is always three-dimensional with disturbances which connect to the two-dimensional waves in the limit of zero groove amplitude playing the critical role. The presence of grooves destabilizes the flow if the groove wavenumber $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\beta $ is larger than $\beta _{tran}\approx 4.22$, but stabilizes the flow for smaller $\beta $. It has been found that $\beta _{tran}$ does not depend on the groove amplitude. The dependence of the critical Reynolds number on the groove amplitude and wavenumber has been determined. Special attention has been paid to the drag-reducing long-wavelength grooves, including the optimal grooves. It has been demonstrated that such grooves slightly increase the critical Reynolds number, i.e. such grooves do not cause an early breakdown into turbulence.

ISOCHRONS FOR A THREE‐DIMENSIONAL SEISMIC SYSTEM

Geophysics ◽  
1971 ◽  
Vol 36 (6) ◽  
pp. 1099-1137 ◽  
Author(s):  
J. W. Dunkin ◽  
F. K. Levin
Keyword(s):  
Surface Waves ◽  
Arbitrary Shape ◽  
Average Velocity ◽  
Three Dimensional ◽  
Dimensional System ◽  
Ray Geometry ◽  
Three Dimensional System ◽  
Seismic System

The three‐dimensional seismic system discussed by Walton (1970–1971) explores seismically a column of earth extending from the surface to deep reflectors. Interpretation of data from the system is done directly from displays on a grid of the detected signals. In this paper we derive expressions for the patterns expected on three‐dimensional system displays when energy returning to the detectors consists of reflections from planes, diffractions from faults or point scatterers, reflections from reflectors of arbitrary shape, refractions and reflected‐refractions from planes, or direct or surface waves. Examples of typical patterns are shown. Our derivations are limited to ray geometry and shed no light on amplitude variations. Also, an average velocity from the surface to a reflector, refractor, or diffractor is assumed.

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