scholarly journals Moments and lower bounds in the far-field of solutions to quasi-geostrophic flows

2005 ◽  
Vol 13 (5) ◽  
pp. 1277-1304 ◽  
Author(s):  
Maria Schonbek ◽  
◽  
Tomas Schonbek ◽  
Keyword(s):  
Lower Bounds ◽  
Far Field ◽  
Geostrophic Flows ◽  
Field Of Solutions

Lower Bounds for Sonic Bangs in the Far Field

1967 ◽  
Vol 18 (1) ◽  
pp. 1-21 ◽  
Author(s):  
L. B. Jones
Keyword(s):  
Lower Bounds ◽  
Far Field ◽  
Centre Of Pressure ◽  
Area Distribution ◽  
General Configuration

SummaryIn this paper lower bounds are obtained for the intensity of the sonic bang resulting from a slender aircraft flying straight and level at supersonic speeds. The lower bounds are obtained for an aircraft subject to various constraints on its total lift, volume, area distribution and centre-of-pressure position. The work described proves the results quoted in an earlier paper, corrects the results given in that paper for the general configuration, and extends the results to cover more constraints, mainly the centre-of-pressure position.

Possible applications of fraunhofer holography in high resolution electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 222-223 ◽  
Author(s):  
N. Bonnet ◽  
M. Troyon ◽  
P. Gallion
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Transfer Function ◽  
Radiation Damage ◽  
High Resolution Electron Microscopy ◽  
Far Field ◽  
Field Region ◽  
Crystalline Materials ◽  
Resolution Electron ◽  
The Ideal

Two main problems in high resolution electron microscopy are first, the existence of gaps in the transfer function, and then the difficulty to find complex amplitude of the diffracted wawe from registered intensity. The solution of this second problem is in most cases only intended by the realization of several micrographs in different conditions (defocusing distance, illuminating angle, complementary objective apertures…) which can lead to severe problems of contamination or radiation damage for certain specimens.Fraunhofer holography can in principle solve both problems stated above (1,2). The microscope objective is strongly defocused (far-field region) so that the two diffracted beams do not interfere. The ideal transfer function after reconstruction is then unity and the twin image do not overlap on the reconstructed one.We show some applications of the method and results of preliminary tests.Possible application to the study of cavitiesSmall voids (or gas-filled bubbles) created by irradiation in crystalline materials can be observed near the Scherzer focus, but it is then difficult to extract other informations than the approximated size.

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