Power-law Correlation Function Research Articles

The Large-scale Distribution of Radio Sources

AbstractWe have used a sample of 263 Parkes half-Jansky flat-spectrum radio sources to measure the spatial correlation function of radio galaxies and radio-loud quasars on scales up to 1000 h−1 Mpc. We do not detect any clustering in the sample. If any undetected clustering is described by a power-law spatial correlation function [ξ(r) = (r/r0)−1·8], we can rule out clustering with scales r0 ≥ 50 h−1 Mpc at the 99·9% confidence level. We have also used the sample to test for the ‘possible’ large concentration of quasars in the direction of the microwave background dipole found by Shaver (1987). There is no evidence for such a concentration in our data and we show that the earlier result was probably biased by the use of non-uniform image classifications.

The Dipolar-Correlation Effect on the Stimulated Echo. Application to Polymer Melts

The quotient of the amplitudes of the stimulated and the primary echoes generated by a three-pulse sequence is strongly affected by dipolar coupling if motional averaging is incomplete. This effect can be experimentally discriminated from echo attenuation by relaxation and diffusion. A method is established on this basis which permits studies of molecular order and dynamics. The time scale is particularly long and is limited only by spin–lattice relaxation. A theory is presented which links the echo amplitudes with the dipolar-correlation function. The echo attenuation curves have been calculated for correlation functions decaying according to exponential and power laws. The results are compared with experimental data of entangled poly(ethylene oxide) and poly(dimethylsiloxane) melts. It is shown that power-law correlation functions are a suitable basis for the description of the observed phenomena.

Two-point correlation function, correlation fractal dimension and typical scales in the large-scale distribution of IRAS galaxies

We discuss relation between two-point correlation function and correlation fractal dimension and use the IRAS galaxy redshift survey as illustration. The large-scale (≳ 15–20 h −1Mpc) distribution of the IRAS galaxies can neither be described by a simple power-law two-point correlation function, nor a simple fractal. It can be better represented by a multi-level fractal. One of the characteristics of multi-level fractal is the existence of typical scales, at which fractal level changes. Un-normalized count can be used to determine the typical scales effectively and precisely. The existence of typical scales is a challenge to the current models of structure formation.

Hypersonic acceleration and turbulence of H2O masters in W49N

view Abstract Citations (65) References (44) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Hypersonic Acceleration and Turbulence of H 2O Masers in W49N Gwinn, C. R. Abstract Velocity turbulence and hypersonic acceleration of H2O maser features appear in their distributions in position and velocity. These conclusions are based on five epochs of astrometric Very Long Baseline Interferometry (VLBI) observations of W49N, particulary on the fourth epoch, when more than 250 features were detected. Correlation functions indicate that physical masers features have sizes of 1 AU and velocity scales of 0.5 km/s. Between 1 and 300 AU, maser features show power-law correlation functions suggestive of velocity turbulence. At scales of 300 AU, masers are organized into arcs: associations of features oriented perpendicular to the direction of outflow. Velocities of features, including proper motion as well as Doppler velocity, show a minimum of about 20 km/s. The high Doppler velocities of some features, long observed spectroscopically, represent high physical velocities. High-velocity features lie at the periphery of the maser cluster. The association of high- and low-velocity features on scale of 300 AU, much less than 104 AU diameter of the cluster, suggests that high-velocity features are accelerated in situ. These observations can be understood in a picture where an energetic stellar wind strikes ambient material to produce masers behind shocks. Fluid instabilities in the shocked material, such as the instability of C-shocks discovered by Wardle, may then produce the strong turbulence observed between masers. Ram pressure from this wind could accelerate high-velocity features to the observed hypersonic velocities, as suggested by Strelnitskii & Sunyaev. Publication: The Astrophysical Journal Pub Date: July 1994 DOI: 10.1086/174315 Bibcode: 1994ApJ...429..241G Keywords: Astronomy; Hypersonic Wakes; Turbulent Flow; Water Masers; Coherent Electromagnetic Radiation; Doppler Effect; Flow Velocity; Velocity Distribution; Very Long Base Interferometry; Astrophysics; ASTROMETRY; ISM: INDIVIDUAL ALPHANUMERIC: W49; ISM: KINEMATICS AND DYNAMICS; TURBULENCE full text sources ADS | data products SIMBAD (2)

Replica Boundary Condition Applied to Random Spin Systems

We introduce a new boundary condition conjugate to any ordered phases including the spin glass. Using this boundary condition, we calculate an interfacial free energy in random spin systems, which is always non-negative irrespective of the bond configuration. It is possible to calculate a quantity relevant to the spin glass phase as a statistical average of random bond configurations. We apply this method to the asymmetric ± J Ising model in 2D and 3D. The results are consistent with the previous ones. We observe the scale invariance of the interfacial free energy by the present method at the critical point in 2D ( T =0), which is consistent with the power-law decaying spin glass correlation function.

Non-Gaussian signatures from Gaussian initial fluctuations - Evolution of skewness and kurtosis from cosmological simulations in the highly nonlinear regime

Following recent observational studies of counts-in-cells statistic, we consider the evolution of the third and fourth moments of distribution functions of the density contrast 6. We define a normalized skewness as S = [delta3]/[delta2]2 and a normalized kurtosis as K = ([delta4] - 3 [delta2]2)/[delta2]3, which are expected from previous theoretical and phenomenological arguments to be '' constants '' in the mildly nonlinear regime. We extended the study of S and K into the highly nonlinear regime 1 less than or similar to delta(rms) = [delta2]1/2 less than or similar to 30 using N-body simulations and taking into account the effect of Poisson shot noise. We find that the simple scaling relation which holds in the mildly nonlinear regime breaks down in the highly nonlinear regime. Both S and K exhibit variation which strongly depends on the primordial power spectrum of density fluctuations, but only weakly on the epoch. For a low-density (OMEGA = 0.2; lambda = 0.8) cold dark matter model at the ''present epoch,'' the normalized skewness and kurtosis in cubic cells are well approximated by S(F) almost-equal-to 3 delta(rms)0.4 and K(F) almost-equal-to 15 delta(rms)0.9 (after removing the shot-noise contribution), over the range 1 less than or similar to delta(rms) less than or similar to 27. For a simulation with initial white-noise spectrum the moments vary more slowly, S(F) almost-equal-to 2 delta(rms)0.2 and K(F) almost-equal-to 8 delta(rms)0.3. Our present findings are in conflict with simple hierarchical clustering models with a power-law correlation function which predict that S(F) and K(F) are independent of the scale. Furthermore, we find that in redshift space the moments, as well as S and K, are smaller than in real space for delta(rms) > 1. Consequently S and S(F) appear to be '' constants '' in redshift space analysis which might explain several observational indications in favor of hierarchical clustering models.We also discuss sparse sampling and the effect of filtering scale and shape. Counts-in-cells of IRAS and optical galaxies suggest S approximately 2 for delta(rms) less than or similar to 1, while from the correlation functions of optical galaxies S approximately 4 for delta(rms) greater than or similar to 1. These values are in accord with that expected from gravitational clustering from Gaussian initial conditions and may carry important information on the shape of the power spectrum.

Ultrasonic characterization of fractal models

Ultrasonic scattering in inhomogeneous fluid media is examined. Of particular interest are those media having a compressibility that varies on a continuum of spatial scales. It is shown that the internal features of such media can be extracted by an analysis of the forward scattered field. The angular distribution of scattered pressure intensity is found to vary with frequency and compressibility contrast. The scattered field data can be rendered stationary to such variations by an application of a similarity transformation. Examples are given for cases where the spatial variation in the compressibility of the media obeys either a power law or exponential correlation function. When these similarity transformations are applied, an estimate of the characteristic radius of the scatterers and the fractal dimension of the medium can be directly obtained. >

The variation of large-angle scattered intensity with the different power laws of the permittivity fluctuation correlation function

In a recent paper (see D.A. de Wolf and S.R. Begum, J. Opt. Soc. Am. A., vol.2, no.12, p.2106-11, Dec. 1985), explicit results were calculated for a two-dimensional geometry describing cylindrical scattering from a slab of width L filled with a uniformly turbulent dielectric described by the Kolmogorov spectrum. The results show that there is an enhancement in the scattered flux compared to the Born-approximated flux due to the inclusion of cumulative effects of small-angle scatterings. This result is extended in the present work for a generalized power law correlation function of the dielectric permittivity fluctuations. It is shown that the cumulative forward and single large-angle scattered flux is somewhat sensitive to the statistical properties of a random continuum in the inertial subrange.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Propagation of waves in a randomly inhomogeneous medium with strongly developed fluctuations. III. Arbitrary power-law noise correlation function

Propagation of waves in a randomly inhomogeneous medium with strongly developed fluctuations. III. Arbitrary power-law noise correlation function

High-resolution x-ray-scattering study of the commensurate-incommensurate transition of monolayer Kr on graphite

We report a detailed high-resolution, x-ray-scattering study of the commensurate-incommensurate transition of Kr on $\mathrm{ZYX}$ exfoliated graphite powder. As the Kr coverage is increased, the transition proceeds as follows: A sharp diffraction line from the commensurate phase drops in intensity and is replaced by a diffuse incommensurate line. The scattering from this disordered phase sharpens continuously as it moves to higher wave vector. We have followed this evolution up to 4% compression, where the line shape is adequately described by a power-law correlation function characteristic of two-dimensional solids. In one sample, there was a significant two-phase coexistence region which we ascribe to a distribution of critical points. We place an upper limit of 1% on the possible first-order jump. No evidence for a uniaxially compressed phase is seen. The weakly incommensurate diffraction line is accompanied by a satellite which may arise from either a domain-wall superlattice or a weak strain modulation of the overlayer. A detailed description of domain lattice models is presented. The loss of long-range order at the transition is discussed in the light of current theories.