Experimental Evidence of Quasiperiodicity and Its Breakdown in the Column-Pendulum Oscillator

1995 ◽  
Vol 117 (2) ◽  
pp. 218-225 ◽  
Author(s):  
G. Mustafa ◽  
A. Ertas
Keyword(s):  
Fourier Spectrum ◽  
Invariant Tori ◽  
Flexible Structures ◽  
Experimental System ◽  
Experimental Dynamics ◽  
Resonance Overlap ◽  
Embedding Technique ◽  
Onset Of Turbulence ◽  
Delay Coordinate Embedding ◽  
Coordinate Embedding

A new vibration absorbing device is introduced for large flexible structures. The phase-space of the experimental system is reconstructed via delay-coordinate embedding technique. Experimental dynamics indicate that the motion is predominantly quasiperiodic, confirming the existence of invariant tori. Within the quasi-periodic region, there are windows containing intricate webs of phase-locked periodic responses. The quasiperiodic and the phase-locked responses are clearly visualized on the cover of the torus. Increase in the amplitude of excitation results in distortion of the invariant torus due to the resonance overlap. Due to the resonance overlap, the return map extracted from the experimental data becomes noninvertible. Furthermore, a burst of frequencies appears on the Fourier spectrum. This scenario is similar to many experimental observations of hydrodynamical instabilities; the breakup of the tori in these experiments is related to the onset of turbulence.

EXPERIMENTAL CONTROL OF CHAOS BY MODIFICATIONS OF DELAYED FEEDBACK

2001 ◽  
Vol 11 (12) ◽  
pp. 3125-3132 ◽  
Author(s):  
KAZUYUKI YAGASAKI ◽  
YOSHIYUKI TOCHIO
Keyword(s):  
Experimental System ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Control Technique ◽  
Control Force ◽  
Unstable Periodic Orbits ◽  
System A ◽  
Embedding Technique ◽  
Delay Coordinate Embedding ◽  
Coordinate Embedding

We present two modifications of the delayed feedback control technique for controlling chaotic dynamical systems. In these methods, control force is applied only when trajectories enter neighborhoods of the targets. So three shortcomings in the delayed feedback technique, the nonsmallness of control force, impossibility of targeting unstable periodic orbits and birth of undesirable stable orbits, are improved. The delay coordinate embedding technique is also used for specifying the target orbits and determining whether trajectories enter their neighborhood. We demonstrate the effectiveness of the two approaches for an experimental system, a feedback controlled pendulum.

Explicit Realization of Chaos Control in an NMR-Laser Experiment

1993 ◽  
Vol 48 (5-6) ◽  
pp. 627-628
Author(s):  
J. Parisi ◽  
R. Badii ◽  
E. Brun ◽  
L. Flepp ◽  
C. Reyl ◽  
...  
Keyword(s):  
Control Method ◽  
Laser System ◽  
Small Time ◽  
System Quality ◽  
Real Time Control ◽  
Time Control ◽  
Explicit Realization ◽  
Delay Coordinate Embedding ◽  
The Stability ◽  
Coordinate Embedding

Abstract The usefulness of the Ott-Grebogi-Yorke control method is demonstrated by stabilizing a chaotic NMR-laser system around an unstable period-one orbit. We have used a six-dimensional delay-coordinate embedding technique in order to fully determine the stability properties of the orbit controlled. Our analysis yields small time-dependent perturbations of the system quality factor capable to perform real-time control.

Recent Developments in Chaotic Time Series Analysis

2003 ◽  
Vol 13 (06) ◽  
pp. 1383-1422 ◽  
Author(s):  
Ying-Cheng Lai ◽  
Nong Ye
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Hilbert Transform ◽  
Chaotic Time Series ◽  
Unstable Periodic Orbits ◽  
Series Analysis ◽  
Delay Coordinate Embedding ◽  
The Hilbert Transform ◽  
Chaotic Time Series Analysis ◽  
Coordinate Embedding

In this paper, two issues are addressed: (1) the applicability of the delay-coordinate embedding method to transient chaotic time series analysis, and (2) the Hilbert transform methodology for chaotic signal processing.A common practice in chaotic time series analysis has been to reconstruct the phase space by utilizing the delay-coordinate embedding technique, and then to compute dynamical invariant quantities of interest such as unstable periodic orbits, the fractal dimension of the underlying chaotic set, and its Lyapunov spectrum. As a large body of literature exists on applying the technique to time series from chaotic attractors, a relatively unexplored issue is its applicability to dynamical systems that exhibit transient chaos. Our focus will be on the analysis of transient chaotic time series. We will argue and provide numerical support that the current delay-coordinate embedding techniques for extracting unstable periodic orbits, for estimating the fractal dimension, and for computing the Lyapunov exponents can be readily adapted to transient chaotic time series.A technique that is gaining an increasing attention is the Hilbert transform method for signal processing in nonlinear systems. The general goal of the Hilbert method is to assess the spectrum of the instantaneous frequency associated with the underlying dynamical process. To obtain physically meaningful results, it is necessary for the signal to possess a proper rotational structure in the complex plane of the analytic signal constructed by the original signal and its Hilbert transform. We will describe a recent decomposition procedure for this task and apply the technique to chaotic signals. We will also provide an example to demonstrate that the methodology can be useful for addressing some fundamental problems in chaotic dynamics.

Visualization of the Platelet-Plasma Interface

1977 ◽  
Vol 35 ◽  
pp. 494-495
Author(s):  
D. C. Brindley ◽  
M. McGill
Keyword(s):  
Platelet Rich Plasma ◽  
Coagulation Factors ◽  
Platelet Membrane ◽  
Rabbit Platelet ◽  
Surface Coat ◽  
Special Relationship ◽  
Routine Method ◽  
Embedding Technique ◽  
Biochemical Analyses ◽  
Adsorptive Properties

Morphological and cytochemical studies of platelets have reported a surface coat, or glycocalyx, external to the plasma membrane (1). Biochemical analyses have likewise confirmed the highly adsorptive properties of platelets as transporters of coagulation factors (2). However, visualization of the platelet membrane by conventional EM procedures does not reflect this special relationship between the platelet and its plasma environment. By the routine method of alcohol-propylene oxide dehydration for Epon embedding, the lipid bilayer nature of the platelet membrane appears similar to other blood cells (Fig. 1). A new rapid embedding technique using dimethoxypropane (DMP) as dehydrating agent (13) has permitted ultrastructural analyses of the surface features of the platelet-plasma interface.Aliquots of human or rabbit platelet-rich plasma (PRP) were added to equal volumes of 6% glutaraldehyde in Millonig's buffer at 37° for 45 minutes, rinsed in buffer and postfixed in 1% osmium in Millonig's buffer for 45 minutes.

Electron holography in materials science

1991 ◽  
Vol 49 ◽  
pp. 670-671
Author(s):  
Hannes Lichte ◽  
Edgar Voelkl
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Materials Science ◽  
Fourier Spectrum ◽  
Object Wave ◽  
Electron Holography ◽  
Reconstruction Procedure ◽  
Numerical Reconstruction ◽  
Transmission Electron ◽  
Unique Interpretation

The object wave o(x,y) = a(x,y)exp(iφ(x,y)) at the exit face of the specimen is described by two real functions, i.e. amplitude a(x,y) and phase φ(x,y). In stead of o(x,y), however, in conventional transmission electron microscopy one records only the real intensity I(x,y) of the image wave b(x,y) loosing the image phase. In addition, referred to the object wave, b(x,y) is heavily distorted by the aberrations of the microscope giving rise to loss of resolution. Dealing with strong objects, a unique interpretation of the micrograph in terms of amplitude and phase of the object is not possible. According to Gabor, holography helps in that it records the image wave completely by both amplitude and phase. Subsequently, by means of a numerical reconstruction procedure, b(x,y) is deconvoluted from aberrations to retrieve o(x,y). Likewise, the Fourier spectrum of the object wave is at hand. Without the restrictions sketched above, the investigation of the object can be performed by different reconstruction procedures on one hologram. The holograms were taken by means of a Philips EM420-FEG with an electron biprism at 100 kV.

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