Symbolic dynamics behind the singular continuous power spectra of continuous flows

1998 ◽  
Vol 117 (1-4) ◽  
pp. 77-94 ◽  
Author(s):  
Michael A. Zaks ◽  
Arkady S. Pikovsky ◽  
Jürgen Kurths
Keyword(s):  
Symbolic Dynamics ◽  
Power Spectra ◽  
Continuous Flows ◽  
Continuous Power

Nonlinear Dynamics of Electrokinetic Instabilities

2005 ◽  
Author(s):  
Jonathan D. Posner ◽  
Juan G. Santiago
Keyword(s):  
Electric Fields ◽  
High Speed ◽  
Power Spectra ◽  
Epifluorescence Microscopy ◽  
Bulk Liquid ◽  
Sample Stacking ◽  
Electrokinetic Instability ◽  
Absolute Flow ◽  
Electrokinetic Flows ◽  
Continuous Power

Electrokinetic instabilities are generated by a coupling of electric fields and ionic conductivity gradients. This coupling results in an electric body force in the bulk liquid that can generate temporal, convective, and absolute flow instabilities. In this work, we perform a parametric experimental study of convective instabilities in cross-shaped microchannels using epifluorescence microscopy and high speed digital imaging. We report temporal power spectra and spatiotemporal maps as a function of the applied field. The spectral analyses reveal that disturbances induced by electrokinetic instability are purely sinuous at the onset of instability and exhibit higher-order harmonics, frequency bifurcations, and continuous power spectra with increasing electric Rayleigh number. Electrokinetic instabilities (EKI) in cross-shaped channels are relevant to injections for field amplified sample stacking, electrokinetic flows at the intersections in multi-dimensional assay devices, and systems with indeterminate sample chemistry.

scholarly journals 8. High Frequency Stellar Oscillations: IV: Photoelectric Monitoring of Southern White Dwarfs

1971 ◽  
Vol 42 ◽  
pp. 41-45
Author(s):  
J. E. Hesser ◽  
B. M. Lasker
Keyword(s):  
Time Series ◽  
High Frequency ◽  
White Dwarfs ◽  
Time Series Data ◽  
Power Spectra ◽  
Series Data ◽  
Period Range ◽  
Stellar Oscillations ◽  
Continuous Power

Time-series data for 14 stars in the list of Eggen and Greenstein have been used to compute their power spectra, which confirm previously found quiescency in the 4 to 700 sec period range. Additionally, characteristics of the continuous power spectra are considered.

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.

D-test: A New Test for Analyzing Scale Invariance Using Symbolic Dynamics and Symbolic Entropy

Methodology ◽  
2011 ◽  
Vol 7 (3) ◽  
pp. 88-95 ◽  
Author(s):  
Jose A. Martínez ◽  
Manuel Ruiz Marín
Keyword(s):  
Symbolic Dynamics ◽  
Scale Invariance ◽  
Rating Scales ◽  
Rating Scale ◽  
Marketing Research ◽  
Response Patterns ◽  
Measurement Scales ◽  
Improve Measurement ◽  
Entropy Measures ◽  
The Difference

The aim of this study is to improve measurement in marketing research by constructing a new, simple, nonparametric, consistent, and powerful test to study scale invariance. The test is called D-test. D-test is constructed using symbolic dynamics and symbolic entropy as a measure of the difference between the response patterns which comes from two measurement scales. We also give a standard asymptotic distribution of our statistic. Given that the test is based on entropy measures, it avoids smoothed nonparametric estimation. We applied D-test to a real marketing research to study if scale invariance holds when measuring service quality in a sports service. We considered a free-scale as a reference scale and then we compared it with three widely used rating scales: Likert-type scale from 1 to 5 and from 1 to 7, and semantic-differential scale from −3 to +3. Scale invariance holds for the two latter scales. This test overcomes the shortcomings of other procedures for analyzing scale invariance; and it provides researchers a tool to decide the appropriate rating scale to study specific marketing problems, and how the results of prior studies can be questioned.

The Software «MMI–calibration 3.0»

Metrologiya ◽  
2020 ◽  
pp. 16-24
Author(s):  
Alexandr D. Chikmarev
Keyword(s):  
Power Series ◽  
Data Processing ◽  
Statistical Treatment ◽  
Correction Function ◽  
Calibration Function ◽  
Measuring Instrument ◽  
Working Standard ◽  
Calibration Protocol ◽  
Error Probabilities ◽  
Continuous Power

A single program has been developed to ensure that the final result of the data processing of the measurement calibration protocol is obtained under normal conditions. The calibration result contains a calibration function or a correction function in the form of a continuous sedate series and a calibration chart based on typical additive error probabilities. Solved the problem of the statistical treatment of the calibration protocol measuring in normal conditions within a single program “MMI–calibration 3.0” that includes identification of the calibration function in a continuous power series of indications of a measuring instrument and chart calibration. An example of solving the problem of calibration of the thermometer by the working standard of the 3rd grade with the help of the “MMI-calibration 3.0” program.

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