Time-Domain Scars: Resolving the Spectral Form Factor in Phase Space

Abstract In the current generations of devices the die and its package are closely integrated to achieve desired performance and form factor. As a result, localization of continuity failures to either the die or the package is a challenging step in failure analysis of such devices. Time Domain Reflectometry [1] (TDR) is used to localize continuity failures. However the accuracy of measurement with TDR is inadequate for effective localization of the failsite. Additionally, this technique does not provide direct 3-Dimenstional information about the location of the defect. Super-conducting Quantum Interference Device (SQUID) Microscope is useful in localizing shorts in packages [2]. SQUID microscope can localize defects to within 5um in the X and Y directions and 35um in the Z direction. This accuracy is valuable in precise localization of the failsite within the die, package or the interfacial region in flipchip assemblies.

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Bifurcations of a Controlled Two-Bar Linkage Motion with Considering Viscous Frictions

Shock and Vibration ◽

10.1155/2011/284103 ◽

2011 ◽

Vol 18 (1-2) ◽

pp. 365-375 ◽

Cited By ~ 1

Author(s):

Qingkai Han ◽

Xueyan Zhao ◽

Xingxiu Li ◽

Bangchun Wen

Keyword(s):

Phase Space ◽

Lyapunov Exponents ◽

Time Domain ◽

Shooting Method ◽

Viscous Friction ◽

Dynamical Model ◽

Chaotic Motions ◽

Amplitude Spectra ◽

Set Up ◽

Joint Motions

In this paper, we investigate the joint viscous friction effects on the motions of a two-bar linkage under controlling of OPCL. The dynamical model of the two-bar linkage with an OPCL controller is firstly set up with considering the two joints' viscous frictions. Thereafter, the motion bifurcations of the two-bar linkage along the values of joint viscous frictions are obtained using shooting method. Then, single-periodic, multiple-periodic, quasi-periodic and chaotic motions of link rotating angles are simulated with given different viscous friction values, and they are illustrated in time domain waveforms, phase space portraits, amplitude spectra and Poincare mapping graphs, respectively. Additionally, for the chaotic case, Lyapunov exponents and hypothesis possibilities of the two joint motions are also estimated.

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Universal spectral form factor for chaotic dynamics

Journal of Physics A General Physics ◽

10.1088/0305-4470/37/3/l02 ◽

2004 ◽

Vol 37 (3) ◽

pp. L31-L37 ◽

Cited By ~ 38

Author(s):

Stefan Heusler ◽

Sebastian Müller ◽

Petr Braun ◽

Fritz Haake

Keyword(s):

Form Factor ◽

Chaotic Dynamics ◽

Spectral Form

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Phase‐space footprints of truncated periodicity: Time domain wave‐oriented data processing

The Journal of the Acoustical Society of America ◽

10.1121/1.409329 ◽

1994 ◽

Vol 95 (5) ◽

pp. 2903-2903

Author(s):

L. Carin ◽

L. B. Felsen ◽

T.‐T. Hsu ◽

D. Kralj

Keyword(s):

Phase Space ◽

Data Processing ◽

Time Domain

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Medicine and the Chaos Theory in Description of Individual and Particular

Journal of New Medical Technologies ◽

10.12737/5892 ◽

2014 ◽

Vol 21 (3) ◽

pp. 27-35

Author(s):

Еськов ◽

V. Eskov ◽

Джумагалиева ◽

L. Dzhumagalieva ◽

Еськов ◽

...

Keyword(s):

Phase Space ◽

Time Domain ◽

Stochastic Systems ◽

Distribution Functions ◽

Continuous Change ◽

Recording Time ◽

Behavior Dynamics ◽

Biomedical Systems ◽

Present Complex ◽

Self Organizing

The article presents three approaches (deterministic, stochastic and chaotic – self-organizing) for studying biomedical systems. The authors show that complex biosystems cann’t be described by deterministic and stochastics because of constant changing parameters xi of a state vector of such systems x=x(t). The fundamental distinguish of deterministic and stochastic systems from chaotic – self-organizing is continuous movement x(t) in phase space of states. The authors also present complex of objects which the authors have been studying for the last 30 years and which conform the type III systems. The particular features of the personalized medicine are presented, that denies possibility of identification of body state at one measurement (a point in a phase space). It is connected with the fact that there is a uniform distribution x(t) in time-domain xi which is revealed in continuous change of distribution functions f(x) for different discrete recording time-domain x(t) at all xi. The authors assert that behavior dynamics of neural networks is similar to work of neuroemulators that is terminated by certainty in quasi-attractor’s volumes.

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