An optical study of turbulence

1970 ◽  
Vol 43 (3) ◽  
pp. 607-635 ◽  
Author(s):  
G. E. Roe
Keyword(s):  
Refractive Index ◽  
Power Spectrum ◽  
Power Spectra ◽  
Mean Flow ◽  
Cavendish Laboratory ◽  
Turbulent Region ◽  
Single Beam ◽  
Beam Method ◽  
A New Technique ◽  
Spatial Power Spectrum

This paper describes theoretical and experimental work carried out at the Cavendish Laboratory of the University of Cambridge. The main object of the work was to develop a new technique for measuring the structure of fluid turbulence.A parallel beam of light is passed through the turbulent region, containing refractive index fluctuations, and analyzed on exit by gratings of periodic transmissivity. Two forms of analysis yield (a) the spatial power spectrum of the refractive index fluctuations in the turbulence, and (b) the velocity distribution within the beam aperture. The method does not disturb the fluid physically, does not depend on the existence of a mean flow velocity, and works well in liquids.One of the limitations of this single-beam method is that it produces information averaged along the path length of the beam in the turbulence, and to overcome this a cross-beam technique, using two beams intersecting at right-angles, has been developed in theory. This method gives the spatial power spectrum of the refractive index fluctuations, as does the single beam method, but the results are characteristic only of the volume of intersection of the beams.The paper first discusses the theory of the single-beam and crossed-beam techniques, and then experimental results obtained with the single-beam method.The turbulent region investigated was a rectangular tank of water, heated from below and cooled from above, producing convective turbulence of high Rayleigh number (4·1 × 108), a system difficult to analyze by conventional methods of measurement, such as the hot-wire anemometer.Spectral density functions (power spectra) of refractive index, and hence in this case temperature fluctuations, have been measured, as have velocity distributions. Statistical analysis of the results also gives useful information about the Eulerian time scale of the turbulent field.

scholarly journals Spatial power spectra of dust across the Local Group: No constraint on disc scale height

2019 ◽  
Vol 492 (2) ◽  
pp. 2663-2682 ◽  
Author(s):  
Eric W Koch ◽  
I-Da Chiang (江宜達) ◽  
Dyas Utomo ◽  
Jérémy Chastenet ◽  
Adam K Leroy ◽  
...  
Keyword(s):  
Power Spectrum ◽  
Power Law ◽  
Large Scale ◽  
Power Spectra ◽  
Far Infrared ◽  
Infrared Emission ◽  
Scale Height ◽  
Turbulent Motion ◽  
Spatial Power Spectrum ◽  
30 Doradus

ABSTRACT We analyse the 1D spatial power spectra of dust surface density and mid to far-infrared emission at $24\!-\!500\, \mu$m in the LMC, SMC, M31, and M33. By forward-modelling the point spread function (PSF) on the power spectrum, we find that nearly all power spectra have a single power-law and point source component. A broken power-law model is only favoured for the LMC 24 μm MIPS power spectrum and is due to intense dust heating in 30 Doradus. We also test for local power spectrum variations by splitting the LMC and SMC maps into 820 pc boxes. We find significant variations in the power-law index with no strong evidence for breaks. The lack of a ubiquitous break suggests that the spatial power spectrum does not constrain the disc scale height. This contradicts claims of a break where the turbulent motion changes from 3D to 2D. The power spectrum indices in the LMC, SMC, and M31 are similar (2.0–2.5). M33 has a flatter power spectrum (1.3), similar to more distant spiral galaxies with a centrally-concentrated H2 distribution. We compare the power spectra of H i, CO, and dust in M31 and M33, and find that H i power spectra are consistently flatter than CO power spectra. These results cast doubt on the idea that the spatial power spectrum traces large scale turbulent motion in nearby galaxies. Instead, we find that the spatial power spectrum is influenced by (1) the PSF on scales below ∼3 times the FWHM, (2) bright compact regions (30 Doradus), and (3) the global morphology of the tracer (an exponential CO disc).

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.

scholarly journals The anisotropy of the power spectrum in periodic cosmological simulations

2021 ◽  
Vol 503 (4) ◽  
pp. 5638-5645
Author(s):  
Gábor Rácz ◽  
István Szapudi ◽  
István Csabai ◽  
László Dobos
Keyword(s):  
Dark Matter ◽  
Power Spectrum ◽  
Large Scale ◽  
Cold Dark Matter ◽  
Initial Conditions ◽  
Power Spectra ◽  
Cosmological Simulations ◽  
Spherical Collapse ◽  
Lower Amplitude ◽  
Hydrodynamical Simulations

ABSTRACT The classical gravitational force on a torus is anisotropic and always lower than Newton’s 1/r2 law. We demonstrate the effects of periodicity in dark matter only N-body simulations of spherical collapse and standard Lambda cold dark matter (ΛCDM) initial conditions. Periodic boundary conditions cause an overall negative and anisotropic bias in cosmological simulations of cosmic structure formation. The lower amplitude of power spectra of small periodic simulations is a consequence of the missing large-scale modes and the equally important smaller periodic forces. The effect is most significant when the largest mildly non-linear scales are comparable to the linear size of the simulation box, as often is the case for high-resolution hydrodynamical simulations. Spherical collapse morphs into a shape similar to an octahedron. The anisotropic growth distorts the large-scale ΛCDM dark matter structures. We introduce the direction-dependent power spectrum invariant under the octahedral group of the simulation volume and show that the results break spherical symmetry.

scholarly journals Demonstrating the Tapered Gridded Estimator (TGE) for the Cosmological HI 21-cm Power Spectrum using 150 MHz GMRT observations

2020 ◽  
Author(s):  
Srijita Pal ◽  
Somnath Bharadwaj ◽  
Abhik Ghosh ◽  
Samir Choudhuri
Keyword(s):  
Power Spectrum ◽  
Unbiased Estimate ◽  
Power Spectra ◽  
Neutral Hydrogen ◽  
Statistical Error ◽  
Temperature Fluctuations ◽  
Radio Frequency Interference ◽  
Rectangular Region ◽  
Angular Power Spectrum ◽  
The Mean

Abstract We apply the Tapered Gridded Estimator (TGE) for estimating the cosmological 21-cm power spectrum from 150 MHz GMRT observations which corresponds to the neutral hydrogen (HI) at redshift z = 8.28. Here TGE is used to measure the Multi-frequency Angular Power Spectrum (MAPS) Cℓ(Δν) first, from which we estimate the 21-cm power spectrum P(k⊥, k∥). The data here are much too small for a detection, and the aim is to demonstrate the capabilities of the estimator. We find that the estimated power spectrum is consistent with the expected foreground and noise behaviour. This demonstrates that this estimator correctly estimates the noise bias and subtracts this out to yield an unbiased estimate of the power spectrum. More than $47\%$ of the frequency channels had to be discarded from the data owing to radio-frequency interference, however the estimated power spectrum does not show any artifacts due to missing channels. Finally, we show that it is possible to suppress the foreground contribution by tapering the sky response at large angular separations from the phase center. We combine the k modes within a rectangular region in the ‘EoR window’ to obtain the spherically binned averaged dimensionless power spectra Δ2(k) along with the statistical error σ associated with the measured Δ2(k). The lowest k-bin yields Δ2(k) = (61.47)2 K2 at k = 1.59 Mpc−1, with σ = (27.40)2 K2. We obtain a 2 σ upper limit of (72.66)2 K2 on the mean squared HI 21-cm brightness temperature fluctuations at k = 1.59 Mpc−1.

scholarly journals Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys

2021 ◽  
Author(s):  
Robin E Upham ◽  
Michael L Brown ◽  
Lee Whittaker
Keyword(s):  
Power Spectrum ◽  
Random Noise ◽  
Power Spectra ◽  
Stage Iv ◽  
Wishart Distribution ◽  
Weak Lensing ◽  
Dependence Structure ◽  
Gaussian Fields ◽  
Non Gaussian ◽  
Parameter Constraints

Abstract We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering and their cross-correlation. Testing its performance on the full sky against the Wishart distribution, which is the exact likelihood under the assumption of Gaussian fields, we find that the Gaussian likelihood returns accurate parameter constraints. This accuracy is robust to the choices made in the likelihood analysis, including the choice of fiducial cosmology, the range of scales included, and the random noise level. We extend our results to the cut sky by evaluating the additional non-Gaussianity of the joint cut-sky likelihood in both its marginal distributions and dependence structure. We find that the cut-sky likelihood is more non-Gaussian than the full-sky likelihood, but at a level insufficient to introduce significant inaccuracy into parameter constraints obtained using the Gaussian likelihood. Our results should not be affected by the assumption of Gaussian fields, as this approximation only becomes inaccurate on small scales, which in turn corresponds to the limit in which any non-Gaussianity of the likelihood becomes negligible. We nevertheless compare against N-body weak lensing simulations and find no evidence of significant additional non-Gaussianity in the likelihood. Our results indicate that a Gaussian likelihood will be sufficient for robust parameter constraints with power spectra from Stage IV weak lensing surveys.

Spectrum analysis of sympathetic nerve activity and blood pressure in conscious rats

1992 ◽  
Vol 263 (5) ◽  
pp. H1348-H1355 ◽  
Author(s):  
P. B. Persson ◽  
H. Stauss ◽  
O. Chung ◽  
U. Wittmann ◽  
T. Unger
Keyword(s):  
Blood Pressure ◽  
Power Spectrum ◽  
Sympathetic Nerve ◽  
Sympathetic Nerve Activity ◽  
Power Spectra ◽  
High Frequency Component ◽  
Bipolar Electrode ◽  
Phase Lag ◽  
Nerve Activity ◽  
Wistar Kyoto

This study tests whether the power spectrum of blood pressure (BP) provides information toward the sympathovagal balance of BP control by comparing the BP (femoral arterial catheter) spectrum with the spectrum of the efferent sympathetic nerve activity (SNA, bipolar electrode around splanchnic nerve). A remarkable resemblance between both spectra was found. A high-frequency component (HF) linked to respiration and a slower fluctuation type between 0.15 and 0.6 Hz (LF) were identified. There was a large and significant coherence only in the HF range of the BP and SNA power spectrum (P < 0.01). The phase lag of SNA and BP was roughly 200 ms. The recordings were repeated during pharmacological blockade in nine Wistar-Kyoto rats (WKY) and nine spontaneously hypertensive rats (SHR). alpha 1-Adrenoceptor blockade (prazosin) reduced the proportional LF power of BP in both rat strains (WKY P < 0.01, SHR P < 0.05) in favor of HF (WKY P < 0.01, SHR P < 0.01). Parasympathetic blockade (methylscopolamine) had no effect on proportions of power. Similarly, there were no significant differences in the proportional HF and LF power spectra of WKY and SHR. These data provide direct evidence for a relationship between the BP and SNA power spectra; however, only the acute changes in the sympathetic tone changed the LF-HF relationship.

Neuronal mechanisms underlying physiological tremor

1978 ◽  
Vol 41 (3) ◽  
pp. 557-571 ◽  
Author(s):  
J. H. Allum ◽  
V. Dietz ◽  
H. J. Freund
Keyword(s):  
Power Spectrum ◽  
Pathological Condition ◽  
Power Spectra ◽  
Motor Units ◽  
Physiological Tremor ◽  
Force Level ◽  
Force Output ◽  
Experimental Conditions ◽  
Single Motor Unit ◽  
Total Fusion

1. Tremor force was recorded during stationary isometric contractions of intrinsic hand muscles of normal subjects. Subjects maintained a steady force level between their thumb and forefinger for 30 s. The force level varied from weak (0.2 kg) to strong contractions (7 kg). These experimental conditions were the same as those in two preceding studies, where single motor-unit activity (14) and the correlation between the discharges of two simultaneously recorded motor units and physiological tremor (11) have been investigated. 2. Two alterations of the power spectra were observed at successively stronger contractions: increase of tremor amplitude and changes in the shape of the power spectrum. At all force levels, the power spectra of tremor force show the well-known decay of tremor amplitude from the lower to the higher frequencies with a local peak at 6--10 Hz. This peak does not show a significant change with respect to frequency when the force level is varied. It is shifted toward lower frequencies in a pathological condition (Parkinsonism) where the recruitment firing rates of the motor units are significantly lower than in the normal. 3. Higher frequencies (greater than 20 Hz) are barely present in the power spectrum during the very weak contractions. They become significant as the contractions become stronger. 4. The steep decay of the power spectrum toward higher frequencies has a similar slope (--43 dB/decade) as the reduction in amplitude of the unfused part of the muscle contractions with increasing stimulus rates (--38 dB/decade). The cutoff of the power spectrum above 25 Hz parallels the achievement of total fusion of muscle twitches above this rate. 5. The results are consistent with the hypothesis that the power spectrum over the range of 6--25 Hz is mainly caused by the unfused parts of the twitch contractions of motor units firing between recruitment (6--8/s) and total fusion of the twitches (25--30/s). The decline of the power spectrum toward higher frequencies can be explained by mechanical damping, which results from increasing fusion of the twitch contractions. The low-frequency part of the power spectrum is assumed to be the result of the slow force deviations produced by changes in the net output of the motoneuron pool. 6. These assumptions were supported by additional animal experiments where the number and rate of force-producing elements could be controlled. Bundles of ventral root filaments innervating cat soleus and gastrocnemius muscles were stimulated synchronously and asynchronously at a number of different rates. The force output of the strain gauge was recorded, filtered, and analyzed in the same way as the human force records. 7. Stimualtion of one nerve bundle at one fixed frequency led to a sharp peak in the power spectrum at that frequency plus peaks of decreasing height representing the harmonics of the stimulation frequency. The height of the peaks decreased at --37 dB/decade. 8...

scholarly journals Anti-symmetric clustering signals in the observed power spectrum

2021 ◽  
Vol 2021 (12) ◽  
pp. 003
Author(s):  
José Fonseca ◽  
Chris Clarkson
Keyword(s):  
Dark Matter ◽  
Power Spectrum ◽  
Euler Equation ◽  
Large Scale ◽  
Signal To Noise Ratio ◽  
Power Spectra ◽  
Large Scale Structure ◽  
Scale Structure ◽  
Signal To Noise ◽  
Peculiar Velocities

Abstract In this paper, we study how to directly measure the effect of peculiar velocities in the observed angular power spectra. We do this by constructing a new anti-symmetric estimator of Large Scale Structure using different dark matter tracers. We show that the Doppler term is the major component of our estimator and we show that we can measure it with a signal-to-noise ratio up to ∼ 50 using a futuristic SKAO HI galaxy survey. We demonstrate the utility of this estimator by using it to provide constraints on the Euler equation.

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