Ray-trace equations through three-dimensional reflective on-axis confocal prolate spheroids

1995 ◽  
Author(s):  
Marija Strojnik
Keyword(s):  
Three Dimensional ◽  
Prolate Spheroids ◽  
Ray Trace

scholarly journals Accumulation of motile elongated micro-organisms in turbulence

2013 ◽  
Vol 739 ◽  
pp. 22-36 ◽  
Author(s):  
Caijuan Zhan ◽  
Gaetano Sardina ◽  
Enkeleida Lushi ◽  
Luca Brandt
Keyword(s):  
Turbulent Flow ◽  
Three Dimensional ◽  
Laminar Flows ◽  
Marine Life ◽  
Prolate Spheroids ◽  
Linear Shear ◽  
Local Shear ◽  
Micro Organisms ◽  
Hydrodynamic Effects ◽  
Preferential Alignment

AbstractWe study the effect of turbulence on marine life by performing numerical simulations of motile micro-organisms, modelled as prolate spheroids, in isotropic homogeneous turbulence. We show that the clustering and patchiness observed in laminar flows, linear shear and vortex flows, are significantly reduced in a three-dimensional turbulent flow mainly because of the complex topology; elongated micro-organisms show some level of clustering in the case of swimmers without any preferential alignment whereas spherical swimmers remain uniformly distributed. Micro-organisms with one preferential swimming direction (e.g. gyrotaxis) still show significant clustering if spherical in shape, whereas prolate swimmers remain more uniformly distributed. Due to their large sensitivity to the local shear, these elongated swimmers react more slowly to the action of vorticity and gravity and therefore do not have time to accumulate in a turbulent flow. These results show how purely hydrodynamic effects can alter the ecology of micro-organisms that can vary their shape and their preferential orientation.

Modeling the impact of wide-azimuth acquisition on subsalt imaging

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM241-SM250 ◽  
Author(s):  
Bruce J. VerWest ◽  
Dechun Lin
Keyword(s):  
Simple Model ◽  
Input Data ◽  
Three Dimensional ◽  
Complex Model ◽  
3D Surface ◽  
Seismic Image ◽  
Ray Trace ◽  
Subsalt Imaging ◽  
Multiple Elimination ◽  
The Impact

Wide-azimuth towed streamer (WATS) acquisition improves the subsalt seismic image by suppressing multiples, improves the results of 3D surface-related-multiple elimination (SRME) processing, and provides more uniform seismic illumination of subsalt targets. A simple model shows that the additional suppression of multiples in the case of WATS acquisition is the result of a natural weighting of the traces going into the stack due to the areal nature of the acquisition. This simple model also shows that the extent of the additional multiple suppression is strongly dependent on the acquisition effort. A sparse acquisition effort will result in little additional multiple suppression. The use of 3D SRME processing is shown to be more accurate in predicting multiples, given input data with multiple azimuths, compared to making similar predictions from narrow-azimuth data. Three-dimensional SRME has the potential to reduce the residual multiples to the same extent as WATS acquisition with a higher acquisition effort. A complex model demonstrates that WATS acquisition does reduce the multiple-generated noise in subsalt images, but 3D SRME processing further reduces the residual multiple noise. The use of 3D SRME may reduce the multiples more than that achieved by increasing the cable half-aperture in the WATS acquisition effort. Finally, ray trace modeling is used to investigate the effect of WATS acquisition on subsurface illumination for subsalt imaging. We show that narrow-azimuth acquisition produces irregularities in subsalt illumination perpendicular to the acquisition direction which are a potential cause of migration noise. WATS acquisition results in higher and more uniform subsalt illumination and, hence, improves the subsalt image by reducing subsalt migration noise.

scholarly journals Compressible potential flows around round bodies: Janzen–Rayleigh expansion inferences

2021 ◽  
Vol 932 ◽  
Author(s):  
Idan S. Wallerstein ◽  
Uri Keshet
Keyword(s):  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Four Dimensions ◽  
Potential Flows ◽  
Prolate Spheroids ◽  
Flow Potential ◽  
Inverse Radius ◽  
Rayleigh Expansion ◽  
Simply Connected

The subsonic, compressible, potential flow around a hypersphere can be derived using the Janzen–Rayleigh expansion (JRE) of the flow potential in even powers of the incident Mach number ${\mathcal {M}}_\infty$ . JREs were carried out with terms polynomial in the inverse radius $r^{-1}$ to high orders in two dimensions, but were limited to order ${\mathcal {M}}_\infty ^{4}$ in three dimensions. We derive general JRE formulae for arbitrary order, adiabatic index and dimension. We find that powers of $\ln (r)$ can creep into the expansion, and are essential in the three-dimensional (3-D) sphere beyond order ${\mathcal {M}}_\infty ^{4}$ . Such terms are apparently absent in the 2-D disk, as we verify up to order ${\mathcal {M}}_\infty ^{100}$ , although they do appear in other dimensions (e.g. at order ${\mathcal {M}}_\infty ^{2}$ in four dimensions). An exploration of various 2-D and 3-D bodies suggests a topological connection, with logarithmic terms emerging when the flow is simply connected. Our results have additional physical implications. They are used to improve the hodograph-based approximation for the flow in front of a sphere. The symmetry-axis velocity profiles of axisymmetric flows around different prolate spheroids are approximately related to each other by a simple, Mach-independent scaling.

Three-dimensional ray-trace model for predicting the performance of flashlamp-pumped laser amplifiers

1997 ◽  
Author(s):  
Kenneth S. Jancaitis ◽  
Scott W. Haney ◽  
David H. Munro ◽  
Geoffroy LeTouze ◽  
Olivier Cabourdin
Keyword(s):  
Three Dimensional ◽  
Laser Amplifiers ◽  
Trace Model ◽  
Ray Trace
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