Nonlinear Acoustics Equations to Third Order. New Stabilization of the Burnett Equations

2006 ◽  
Author(s):  
Lars H. Söderholm
Keyword(s):  
Nonlinear Acoustics ◽  
Burnett Equations ◽  
Third Order ◽  
Acoustics Equations

Consistent Third Order Nonlinear Acoustics

2008 ◽  
Author(s):  
Lars H. Söderholm ◽  
Bengt Enflo ◽  
Claes M. Hedberg ◽  
Leif Kari
Keyword(s):  
Nonlinear Acoustics ◽  
Third Order

Exploration of third-order nonlinear acoustics for projection of narrow-beam lower-frequency underwater beams

2013 ◽  
Author(s):  
Robert M. Koch ◽  
Richard A. Katz ◽  
Allan D. Pierce ◽  
Derke R. Hughes
Keyword(s):  
Nonlinear Acoustics ◽  
Narrow Beam ◽  
Third Order

Exploration of third-order nonlinear acoustics for projection of narrow-beam lower-frequency underwater beams

2013 ◽  
Vol 133 (5) ◽  
pp. 3556-3556
Author(s):  
Robert M. Koch ◽  
Richard A. Katz ◽  
Allan D. Pierce ◽  
Derke R. Hughes
Keyword(s):  
Nonlinear Acoustics ◽  
Narrow Beam ◽  
Third Order

Homogenization of high frequency nonlinear acoustics equations

2000 ◽  
Vol 74 (3-4) ◽  
pp. 311-331 ◽  
Author(s):  
Gregory P. PANASENKO ◽  
Evgueny A. Lapshin
Keyword(s):  
High Frequency ◽  
Nonlinear Acoustics ◽  
Acoustics Equations

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

The influence of third-order interactions on the density profile of associating hard spheres

1997 ◽  
Vol 91 (4) ◽  
pp. 761-767 ◽  
Author(s):  
D. HENDERSON ◽  
S. SOKOŁOWSKI ◽  
R. ZAGORSKI ◽  
A. TROKHYMCHUK
Keyword(s):  
Density Profile ◽  
Hard Spheres ◽  
Third Order
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