Statistical properties of one-dimensional binary sequences with power-law power spectrum

2011 ◽  
Vol 390 (17) ◽  
pp. 2977-2986 ◽  
Author(s):  
Longyan Gong ◽  
Zicong Zhou ◽  
Peiqing Tong ◽  
Shengmei Zhao
Keyword(s):  
Power Spectrum ◽  
Power Law ◽  
Statistical Properties ◽  
Binary Sequences ◽  
One Dimensional

scholarly journals Interferometric Techniques Applied to High Resolution Observation of the Solar Granulation

1979 ◽  
Vol 50 ◽  
pp. 30-1-30-6
Author(s):  
Claude Aime
Keyword(s):  
High Resolution ◽  
Power Spectrum ◽  
Statistical Properties ◽  
Two Dimensional ◽  
Solar Granulation ◽  
One Dimensional ◽  
Resolution Observation ◽  
Stellar Interferometry ◽  
High Resolution Observation

AbstractMichelson,one-dimensional, and two-dimensional apertures are used to obtain the statistical properties of the solar granulation. The calibration of the power spectrum is performed via Michelson stellar interferometry as well as by the use of changes in seeing conditions during speckle-interferometric measurements. The correction of 40 analyses, determined with Fried's parameter ro ranging between 2.5 cm and 11.5 cm, provides satisfactory convergence for frequencies up to 3 cycles per arc second

CORRELATIONS OF PITCHES IN MUSIC

Fractals ◽  
1996 ◽  
Vol 04 (04) ◽  
pp. 547-553 ◽  
Author(s):  
YU SHI
Keyword(s):  
Power Spectrum ◽  
Long Range ◽  
Power Law ◽  
Piano Music ◽  
Fundamental Principle ◽  
Mean Square ◽  
Scaling Exponents ◽  
One Dimensional ◽  
Mean Square Fluctuation ◽  
The Mean

We investigate correlations among pitches in several songs and pieces of piano music. Real values of tones are mapped to positions within a one-dimensional walk. The structure of music, such as beat, measure and stanza, are reflected in the change of scaling exponents of the mean square fluctuation. Usually the pitches within one beat are nearly random, while nontrivial correlations are found within duration around a measure; for longer duration the mean square fluctuation is nearly flat, indicating exact 1/f power spectrum. Some interesting features are observed. Correlations are also studied by treating different tones as different symbols. This kind of correlation cannot reflect the structure of music, though long-range power-law is also discovered. Our results support the viewpoint that the fundamental principle of music is the balance between repetition and contrast.

Transient convective diffusion to a uniformly accessible surface under aparent slip conditions

1991 ◽  
Vol 56 (2) ◽  
pp. 334-343
Author(s):  
Ondřej Wein
Keyword(s):  
Power Law ◽  
Analytical Solutions ◽  
Convective Diffusion ◽  
Active Surface ◽  
Velocity Profiles ◽  
One Dimensional ◽  
Slip Conditions ◽  
Accessible Surface ◽  
Diffusion Problems

Analytical solutions are given to a class of unsteady one-dimensional convective-diffusion problems assuming power-law velocity profiles close to the transport-active surface.

scholarly journals Sudden Expansion of a One-Dimensional Bose Gas from Power-Law Traps

2015 ◽  
Vol 114 (12) ◽  
Author(s):  
A. S. Campbell ◽  
D. M. Gangardt ◽  
K. V. Kheruntsyan
Keyword(s):  
Power Law ◽  
Bose Gas ◽  
Sudden Expansion ◽  
One Dimensional

scholarly journals Restoring phase coherence in a one-dimensional superconductor using power-law electron hopping

2013 ◽  
Vol 88 (13) ◽  
Author(s):  
Alejandro M. Lobos ◽  
Masaki Tezuka ◽  
Antonio M. García-García
Keyword(s):  
Power Law ◽  
Phase Coherence ◽  
Electron Hopping ◽  
One Dimensional

scholarly journals Critical flow and dissipation in a quasi–one-dimensional superfluid

2015 ◽  
Vol 1 (4) ◽  
pp. e1400222 ◽  
Author(s):  
Pierre-François Duc ◽  
Michel Savard ◽  
Matei Petrescu ◽  
Bernd Rosenow ◽  
Adrian Del Maestro ◽  
...  
Keyword(s):  
Power Law ◽  
Capillary Flow ◽  
Three Dimensional ◽  
Universality Class ◽  
Superfluid State ◽  
One Dimensional ◽  
Flow Experiment ◽  
20 Nm ◽  
Bulk Behavior ◽  
Superfluid Velocity

In one of the most celebrated examples of the theory of universal critical phenomena, the phase transition to the superfluid state of 4He belongs to the same three-dimensional (3D) O(2) universality class as the onset of ferromagnetism in a lattice of classical spins with XY symmetry. Below the transition, the superfluid density ρs and superfluid velocity vs increase as a power law of temperature described by a universal critical exponent that is constrained to be identical by scale invariance. As the dimensionality is reduced toward 1D, it is expected that enhanced thermal and quantum fluctuations preclude long-range order, thereby inhibiting superfluidity. We have measured the flow rate of liquid helium and deduced its superfluid velocity in a capillary flow experiment occurring in single 30-nm-long nanopores with radii ranging down from 20 to 3 nm. As the pore size is reduced toward the 1D limit, we observe the following: (i) a suppression of the pressure dependence of the superfluid velocity; (ii) a temperature dependence of vs that surprisingly can be well-fitted by a power law with a single exponent over a broad range of temperatures; and (iii) decreasing critical velocities as a function of decreasing radius for channel sizes below R ≃ 20 nm, in stark contrast with what is observed in micrometer-sized channels. We interpret these deviations from bulk behavior as signaling the crossover to a quasi-1D state, whereby the size of a critical topological defect is cut off by the channel radius.

LONG RANGE CORRELATION PROPERTIES OF AFTERSHOCK RELAXATION SIGNALS

Fractals ◽  
1995 ◽  
Vol 03 (04) ◽  
pp. 839-847 ◽  
Author(s):  
A. VESPIGNANI ◽  
A. PETRI ◽  
A. ALIPPI ◽  
G. PAPARO ◽  
M. COSTANTINI
Keyword(s):  
Time Series ◽  
Acoustic Emission ◽  
Statistical Analysis ◽  
Power Spectrum ◽  
Power Law ◽  
Amplitude Distribution ◽  
Relaxation Processes ◽  
Critical Dynamics ◽  
Range Correlation ◽  
Correlation Properties

Relaxation processes taking place after microfracturing of laboratory samples give rise to ultrasonic acoustic emission signals. Statistical analysis of the resulting time series has revealed many features which are characteristic of critical phenomena. In particular, the autocorrelation functions obey a power-law behavior, implying a power spectrum of the kind 1/f. Also the amplitude distribution N(V) of such signals follows a power law, and the obtained exponents are consistent with those found in other experiments: N(V) dV≃V–γ dV, with γ=1.7±0.2. We also analyzed the distribution N(τ) of the delay time τ between two consecutive acoustic emission events. We found that a N(τ) distribution rather close to a power law constitutes a common feature of all the recorded signals. These experimental results can be considered as a striking evidence for a critical dynamics underlying the microfracturing processes.

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