Role of high-order anharmonic terms in the theory of vacancy formation volume

1984 ◽  
Vol 3 (2) ◽  
pp. 263-288 ◽  
Author(s):  
M. Omini
Keyword(s):  
High Order ◽  
Vacancy Formation

On the Role of High-Order Multiple Scattering Terms in Br K-Edge XANES of the Ionic Conductor AgBr

1993 ◽  
Vol 176 (2) ◽  
pp. 503-510 ◽  
Author(s):  
A. V. Soldatov ◽  
T. S. Ivanchenko ◽  
S. Della Longa ◽  
A. Bianconi
Keyword(s):  
Multiple Scattering ◽  
High Order ◽  
Ionic Conductor

Characteristics in Response Integration and Bifurcation of a Forced Duffing Oscillator

2007 ◽  
Author(s):  
Jang-Der Jeng ◽  
Yuan Kang ◽  
Yeon-Pun Chang ◽  
Shyh-Shyong Shyr
Keyword(s):  
Applied Sciences ◽  
Phase Plane ◽  
Duffing Oscillator ◽  
High Order ◽  
Chaotic Motions ◽  
Integration Algorithm ◽  
High Order Harmonic ◽  
Stiffness And Damping

The Duffing oscillator is well-known models of nonlinear system, with applications in many fields of applied sciences and engineering. In this paper, a response integration algorithm is proposed to analyze high-order harmonic and chaotic motions in this oscillator for modeling rotor excitations. This method numerically integrates the distance between state trajectory and the origin in the phase plane during a specific period and predicted intervals with excitation periods. It provides a quantitative characterization of system responses and can replace the role of the traditional stroboscopic technique (Poincare´ section method) to observe bifurcations and chaos of the nonlinear oscillators. Due to the signal response contamination of system, thus it is difficult to identify the high-order responses of the subharmonic motion because of the sampling points on Poincare´ map too near each other. Even the system responses will be made misjudgments. Combining the capability of precisely identifying period and constructing bifurcation diagrams, the advantages of the proposed response integration method are shown by case studies. Applying this method, the effects of the change in the stiffness and the damping coefficients on the vibration features of a Duffing oscillator are investigated in this paper. From simulation results, it is concluded that the stiffness and damping of the system can effectively suppress chaotic vibration and reduce vibration amplitude.

scholarly journals Role of high-order aberrations in senescent changes in spatial vision

2009 ◽  
Vol 9 (2) ◽  
pp. 24-24 ◽  
Author(s):  
S. L. Elliott ◽  
S. S. Choi ◽  
N. Doble ◽  
J. L. Hardy ◽  
J. W. Evans ◽  
...  
Keyword(s):  
Spatial Vision ◽  
High Order ◽  
High Order Aberrations
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