On the equivalence of geometrical-optics reflected fields and the stationary-phase solution of the associated radiation integrals

2002 ◽  
Vol 44 (5) ◽  
pp. 120-123 ◽  
Author(s):  
A.J. Booysen
Keyword(s):  
Stationary Phase ◽  
Geometrical Optics ◽  
Phase Solution

scholarly journals A stationary phase solution for mountain waves with application to mesospheric mountain waves generated by Auckland Island

2017 ◽  
Vol 122 (2) ◽  
pp. 699-711 ◽  
Author(s):  
Dave Broutman ◽  
Stephen D. Eckermann ◽  
Harold Knight ◽  
Jun Ma
Keyword(s):  
Stationary Phase ◽  
Mountain Waves ◽  
Auckland Island ◽  
Phase Solution

Radiation from seismic sources in cased and cemented boreholes

Geophysics ◽  
1994 ◽  
Vol 59 (4) ◽  
pp. 518-533 ◽  
Author(s):  
Richard L. Gibson
Keyword(s):  
Boundary Condition ◽  
Stationary Phase ◽  
Axial Stress ◽  
Broad Band ◽  
Low Frequency ◽  
Seismic Sources ◽  
Radiation Patterns ◽  
S Waves ◽  
Impedance Contrast ◽  
Phase Solution

Far‐field, stationary phase approximations are often used to study the radiation of P‐ and S‐waves from seismic sources located in boreholes, usually with an assumption of low frequency and in application to uncased boreholes. These two assumptions allow explicit analytical results for the radiation patterns to be derived, as boundary condition equations can be solved analytically in fairly simple forms. Applying the same methodology to cased and cemented boreholes, however, is much more difficult because of the increased number of simultaneous boundary condition equations. I circumvent this difficulty by solving the boundary condition equations numerically using propagator matrices, as is generally done in the calculation of synthetic full‐waveform acoustic logs. In this way, the assumption of low frequency is also avoided, and a generalized stationary‐phase solution for sources in general, concentrically layered borehole models is easily obtained. Computation of the radiation patterns for cased and uncased boreholes in various formations shows that the amplitude reduction, because of the introduction of casing, is a function of both source type and of formation velocities. Axial stress sources are less affected by the casing than either radial stress or volume‐injection sources, and as formation velocity decreases, the effect of the casing becomes more significant as the impedance contrast between steel and the formation becomes larger. The new generalized stationary‐phase solution also shows that as frequency approaches 1000 Hz, the results obtained by low‐frequency approximations for stress sources can be inaccurate and that the energy radiated from the source becomes more highly directed in the horizontal directions. The radiation pattern begins to change relatively rapidly as a function of frequency, so that the resulting observations from broad‐band sources will show changes in waveforms that mimic the effects of attenuation. These changes occur because the length of the source becomes important as wavelength decreases, demonstrating the need to consider the influence of frequency, as well as casing and cement, on source radiation.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

Waves in weakly anisotropic 3D inhomogeneous media: quasi-isotropic approximation of geometrical optics

1996 ◽  
Vol 166 (2) ◽  
pp. 141-167 ◽  
Author(s):  
Yu.A. Kravtsov ◽  
O.N. Naida ◽  
A.A. Fuki
Keyword(s):  
Geometrical Optics ◽  
Inhomogeneous Media ◽  
Isotropic Approximation

The Determination of Shortwave Asymptotics of Scattered Fields by the Stationary-Phase Method

2000 ◽  
Vol 54 (7) ◽  
pp. 14-22 ◽  
Author(s):  
Il'ya Vladimirovich Sukharevskii ◽  
Oleg ll'ich Sukharevsky
Keyword(s):  
Stationary Phase ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Scattered Fields

Chiral drugs separation by a new antibiotics-based chiral stationary phase

2014 ◽  
Author(s):  
Chunye Liu ◽  
Yanqing Miao ◽  
Yihui Guo ◽  
Yinjuan An ◽  
Yunfang Li ◽  
...  
Keyword(s):  
Stationary Phase ◽  
Chiral Stationary Phase ◽  
Chiral Drugs ◽  
New Antibiotics
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