An approximate nonlinear dynamic theory for plates

1971 ◽  
Vol 5 (1) ◽  
pp. 99-107
Author(s):  
O. E. Widera
Keyword(s):  
Nonlinear Dynamic ◽  
Dynamic Theory

scholarly journals Nonlinear dynamic theory for photorefractive phase hologram formation

1976 ◽  
Vol 28 (6) ◽  
pp. 338-340 ◽  
Author(s):  
Dae M. Kim ◽  
Rajiv R. Shah ◽  
T. A. Rabson ◽  
F. K. Tittel
Keyword(s):  
Nonlinear Dynamic ◽  
Dynamic Theory ◽  
Phase Hologram

scholarly journals Applying nonlinear dynamic theory to one-dimensional pulsating detonations

2011 ◽  
Vol 15 (2) ◽  
pp. 205-225 ◽  
Author(s):  
Hamid Ait Abderrahmane ◽  
Frederick Paquet ◽  
Hoi Dick Ng
Keyword(s):  
Nonlinear Dynamic ◽  
Dynamic Theory ◽  
One Dimensional

An Example of How Nonlinear Dynamics Tools Can be Successfully Applied to A Chemical System

Fractals ◽  
1997 ◽  
Vol 05 (03) ◽  
pp. 531-547 ◽  
Author(s):  
L. Pellegrini ◽  
C. Tablino Possio ◽  
G. Biardi
Keyword(s):  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Bifurcation Theory ◽  
Dynamic Theory ◽  
Stirred Tank ◽  
Chemical System ◽  
Controlling Chaos ◽  
Practical Applications ◽  
Tank Reactor ◽  
Continuously Stirred Tank Reactor

The nonlinear dynamic behavior of a Proportional-Integral controlled Continuously Stirred Tank Reactor (CSTR) is analyzed in depth progressing from chaos characterization, through the high codimension bifurcation theory, up to the application of Controlling Chaos techniques. All these tools can be successfully applied to recognize, to avoid and to use chaos in practical applications, so that the nonlinear dynamic theory turns out to be an indispensable science to constrain dynamic systems to work in the most suitable operative conditions.

Calculation of many-beam dynamic electron diffraction without high-energy approximation

1996 ◽  
Vol 54 ◽  
pp. 128-129
Author(s):  
B. R. Ahn ◽  
N. J. Kim
Keyword(s):  
Electron Diffraction ◽  
Flat Surface ◽  
Dynamic Theory ◽  
High Energy ◽  
Perfect Crystal ◽  
Zone Axis ◽  
Beam Dynamic ◽  
Diffraction Angle ◽  
Energy Approximation ◽  
The Many

High energy approximation in dynamic theory of electron diffraction involves some intrinsic problems. First, the loss of theoretical strictness makes it difficult to comprehend the phenomena of electron diffraction. Secondly, it is difficult to believe that the approximation is reasonable especially in the following cases: 1) when accelerating voltage is not sufficiently high, 2) when the specimen is thick, 3) when the angle between the surface normal of the specimen and zone axis is large, and 4) when diffracted beam with large diffraction angle is included in the calculation. However, until now the method to calculate the many beam dynamic electron diffraction without the high energy approximation has not been proposed. For this reason, the authors propose a method to eliminate the high energy approximation in the calculation of many beam dynamic electron diffraction. In this method, a perfect crystal with flat surface was assumed. The method was applied to the calculation of [111] zone axis CBED patterns of Si.

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