Power Spectra of the Intermittent Chaos Generated by the Quadratic Tangent Bifurcation

1984 ◽  
Vol 72 (6) ◽  
pp. 1258-1261 ◽  
Author(s):  
B. C. So ◽  
H. Mori
Keyword(s):  
Power Spectra ◽  
Tangent Bifurcation ◽  
Intermittent Chaos

scholarly journals Power Spectra of Intermittent Chaos Due to the Collapse of Period-3 Windows

1988 ◽  
Vol 79 (6) ◽  
pp. 1260-1264 ◽  
Author(s):  
N. Mori ◽  
S. Kuroki ◽  
H. Mori
Keyword(s):  
Power Spectra ◽  
Intermittent Chaos

scholarly journals Bifurcation in Hydrodynamic Models of Stellar Pulsation

1993 ◽  
Vol 134 ◽  
pp. 269-280
Author(s):  
T. Aikawa
Keyword(s):  
Period Doubling ◽  
Radial Pulsation ◽  
Agb Stars ◽  
Control Parameters ◽  
Hydrodynamic Models ◽  
Nonlinear Pulsation ◽  
Stellar Pulsation ◽  
Classical Cepheids ◽  
Tangent Bifurcation ◽  
Intermittent Chaos

AbstractPhenomena of bifurcation in hydrodynamic stellar models of radial pulsation are reviewed. By changing control parameters of models, we can see qualitatively different pulsation behaviors in hydrodynamic models with transitions due to various types of bifurcation.In weakly dissipative models (classical Cepheids). the bifurcation is induced by modal resonances. Two types of the modal resonances found in models are discussed: The higher-harmonic resonances of the second overtone mode in the fundamental mode pulsator and of the fourth overtone mode in the first overtone pulsator are relevant to observations. The subharmonic resonance between the fundamental and first overtone modes is confirmed in classical Cepheid models.In strongly dissipative models (less-massive supergiant stars), the bifurcation of nonlinear pulsation is induced by the hydrodynamics of ionization zones as well as modal resonances. The sequence of the bifurcation sometimes leads to chaotic behaviors in nonlinear pulsation. The transition routes from regular to the chaotic pulsations found in models are discussed with respect to the theory of chaos in simple dynamical systems: The cascade of period-doubling bifurcation is confirmed to cause chaotic pulsation in W Virginis models. For models of higher luminosity, the tangent bifurcation is found to lead intermittent chaos.Finally, hydrodynamic models for chaotic pulsation with small amplitudes observed in the post-AGB stars are briefly discussed.

scholarly journals Study on Nonlinear Phenomena in Buck-Boost Converter with Switched-Inductor Structure

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hongchen Liu ◽  
Shuang Yang
Keyword(s):  
Period Doubling ◽  
Boost Converter ◽  
Phase Portraits ◽  
Nonlinear Phenomena ◽  
Mapping Model ◽  
Tangent Bifurcation ◽  
Value Range ◽  
The Time Domain ◽  
Intermittent Chaos ◽  
Voltage Conversion

The switched-inductor structure can be inserted into a traditional Buck-Boost converter to get a high voltage conversion ratio. Nonlinear phenomena may occur in this new converter, which might well lead the system to be unstable. In this paper, a discrete iterated mapping model is established when the new Buck-Boost converter is working at continuous conduction current-controlled mode. On the basis of the discrete model, the bifurcation diagrams and Poincare sections are drawn and then used to analyze the effects of the circuit parameters on the performances. It can be seen clearly that various kinds of nonlinear phenomena are easy to occur in this new converter, including period-doubling bifurcation, border collision bifurcation, tangent bifurcation, and intermittent chaos. Value range of the circuit parameters that may cause bifurcations and chaos are also discussed. Finally, the time-domain waveforms, phase portraits, and power spectrum are obtained by using Matlab/Simulink, which validates the theoretical analysis results.

Image formation analysis of thick biological specimens using three-dimensional power-spectra of through focus series

1994 ◽  
Vol 52 ◽  
pp. 124-125
Author(s):  
Karen F. Han
Keyword(s):  
Inelastic Scattering ◽  
Imaging Techniques ◽  
Mass Density ◽  
Relative Proportion ◽  
Three Dimensional ◽  
Power Spectra ◽  
Image Formation ◽  
Energy Filtering ◽  
Ewald Sphere ◽  
Nonlinear Imaging

The primary focus in our laboratory is the study of higher order chromatin structure using three dimensional electron microscope tomography. Three dimensional tomography involves the deconstruction of an object by combining multiple projection views of the object at different tilt angles, image intensities are not always accurate representations of the projected object mass density, due to the effects of electron-specimen interactions and microscope lens aberrations. Therefore, an understanding of the mechanism of image formation is important for interpreting the images. The image formation for thick biological specimens has been analyzed by using both energy filtering and Ewald sphere constructions. Surprisingly, there is a significant amount of coherent transfer for our thick specimens. The relative amount of coherent transfer is correlated with the relative proportion of elastically scattered electrons using electron energy loss spectoscopy and imaging techniques.Electron-specimen interactions include single and multiple, elastic and inelastic scattering. Multiple and inelastic scattering events give rise to nonlinear imaging effects which complicates the interpretation of collected images.

Log-log scale roughness spectroscopy of surfaces

1993 ◽  
Vol 51 ◽  
pp. 224-225
Author(s):  
P. Fraundorf ◽  
B. Armbruster
Keyword(s):  
Power Spectrum ◽  
Autocorrelation Function ◽  
Power Spectra ◽  
Scanning Force Microscopy ◽  
Scanning Tunneling ◽  
Tunneling Microscopy ◽  
Force Microscopy ◽  
Scanning Force ◽  
Lateral Structure ◽  
Scale Roughness

Optical interferometry, confocal light microscopy, stereopair scanning electron microscopy, scanning tunneling microscopy, and scanning force microscopy, can produce topographic images of surfaces on size scales reaching from centimeters to Angstroms. Second moment (height variance) statistics of surface topography can be very helpful in quantifying “visually suggested” differences from one surface to the next. The two most common methods for displaying this information are the Fourier power spectrum and its direct space transform, the autocorrelation function or interferogram. Unfortunately, for a surface exhibiting lateral structure over several orders of magnitude in size, both the power spectrum and the autocorrelation function will find most of the information they contain pressed into the plot’s origin. This suggests that we plot power in units of LOG(frequency)≡-LOG(period), but rather than add this logarithmic constraint as another element of abstraction to the analysis of power spectra, we further recommend a shift in paradigm.

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