On the cross-correlation function of a nonlinear network

1977 ◽  
Vol 65 (11) ◽  
pp. 1615-1616 ◽  
Author(s):  
M. Rudko
Keyword(s):  
Correlation Function ◽  
Cross Correlation ◽  
Cross Correlation Function ◽  
Nonlinear Network ◽  
The Cross

Simultaneous Measurement of Temperature and Velocity Using µPIV

2006 ◽  
Author(s):  
Pramod Chamarthy ◽  
Steven T. Wereley ◽  
Suresh V. Garimella
Keyword(s):  
Brownian Motion ◽  
Correlation Function ◽  
Cross Correlation ◽  
Cross Correlation Function ◽  
Motion Information ◽  
Peak Broadening ◽  
Constant Temperature Water Bath ◽  
Gravity Driven ◽  
The Cross ◽  
Gravity Driven Flow

In μPIV, for a uniform velocity field the displacement of the cross-correlation function gives the velocity of the fluid and the broadening of the peak-width represents the amount of Brownian motion present. In the presence of a linear or a parabolic shear, the shape of the cross-correlation function would have both the Brownian motion information as well as the velocity distribution information. In the present work, the broadening of the cross-correlation function caused by the velocity gradient was subtracted from the total peak broadening in order to isolate the Brownian motion information and thus infer temperature. To the authors' knowledge, this technique has not been applied to measure the temperature of a moving fluid. The experiments were conducted in a gravity driven flow through a tube surrounded by a constant temperature water bath.

Damage Detection Based on the Cross Correlation Function Amplitude Vector and its Application to the ASCE Benchmark Structure

2007 ◽  
Vol 353-358 ◽  
pp. 2317-2320 ◽  
Author(s):  
Zhe Feng Yu ◽  
Zhi Chun Yang
Keyword(s):  
Correlation Function ◽  
Damage Detection ◽  
Structural Damage ◽  
Cross Correlation ◽  
Relative Difference ◽  
Random Excitation ◽  
Cross Correlation Function ◽  
Vibration Responses ◽  
Specific Frequency ◽  
The Cross

A new method for structural damage detection based on the Cross Correlation Function Amplitude Vector (CorV) of the measured vibration responses is presented. Under a stationary random excitation with a specific frequency spectrum, the CorV of the structure only depends on the frequency response function matrix of the structure, so the normalized CorV has a specific shape. Thus the damage can be detected and located with the correlativity and the relative difference between CorVs of the intact and damaged structures. With the benchmark problem sponsored by ASCE Task Group on Structural Health Monitoring, the CorV is proved an effective approach to detecting the damage in structures subject to random excitations.

scholarly journals Revisiting Proxima with ESPRESSO

2020 ◽  
Vol 639 ◽  
pp. A77 ◽  
Author(s):  
A. Suárez Mascareño ◽  
J. P. Faria ◽  
P. Figueira ◽  
C. Lovis ◽  
M. Damasso ◽  
...  
Keyword(s):  
Correlation Function ◽  
Radial Velocity ◽  
Cross Correlation ◽  
Full Width Half Maximum ◽  
Cross Correlation Function ◽  
Minimum Mass ◽  
Full Width ◽  
Half Maximum ◽  
Stellar Activity ◽  
The Cross

Context. The discovery of Proxima b marked one of the most important milestones in exoplanetary science in recent years. Yet the limited precision of the available radial velocity data and the difficulty in modelling the stellar activity calls for a confirmation of the Earth-mass planet. Aims. We aim to confirm the presence of Proxima b using independent measurements obtained with the new ESPRESSO spectrograph, and refine the planetary parameters taking advantage of its improved precision. Methods. We analysed 63 spectroscopic ESPRESSO observations of Proxima (Gl 551) taken during 2019. We obtained radial velocity measurements with a typical radial velocity photon noise of 26 cm s−1. We combined these data with archival spectroscopic observations and newly obtained photometric measurements to model the stellar activity signals and disentangle them from planetary signals in the radial velocity (RV) data. We ran a joint Markov chain Monte Carlo analysis on the time series of the RV and full width half maximum of the cross-correlation function to model the planetary and stellar signals present in the data, applying Gaussian process regression to deal with the stellar activity signals. Results. We confirm the presence of Proxima b independently in the ESPRESSO data and in the combined ESPRESSO+ HARPS+UVES dataset. The ESPRESSO data on its own shows Proxima b at a period of 11.218 ± 0.029 days, with a minimum mass of 1.29 ± 0.13 M⊕. In the combined dataset we measure a period of 11.18427 ± 0.00070 days with a minimum mass of 1.173 ± 0.086 M⊕. We get a clear measurement of the stellar rotation period (87 ± 12 d) and its induced RV signal, but no evidence of stellar activity as a potential cause for the 11.2 days signal. We find some evidence for the presence of a second short-period signal, at 5.15 days with a semi-amplitude of only 40 cm s−1. If caused by a planetary companion, it would correspond to a minimum mass of 0.29 ± 0.08 M⊕. We find that forthe case of Proxima, the full width half maximum of the cross-correlation function can be used as a proxy for the brightness changes and that its gradient with time can be used to successfully detrend the RV data from part of the influence of stellar activity. The activity-induced RV signal in the ESPRESSO data shows a trend in amplitude towards redder wavelengths. Velocities measured using the red end of the spectrograph are less affected by activity, suggesting that the stellar activity is spot dominated. This could be used to create differential RVs that are activity dominated and can be used to disentangle activity-induced and planetary-induced signals. The data collected excludes the presence of extra companions with masses above 0.6 M⊕ at periods shorter than 50 days.

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