The phase-space-resolved two-point correlation function of ion density fluctuations

2005 ◽  
Vol 12 (11) ◽  
pp. 110701 ◽  
Author(s):  
Ahmed Diallo ◽  
Frederick Skiff
Keyword(s):  
Correlation Function ◽  
Phase Space ◽  
Density Fluctuations ◽  
Ion Density ◽  
Point Correlation ◽  
Point Correlation Function

scholarly journals UV background fluctuations and three-point correlations in the large-scale clustering of the Lyman α forest

2019 ◽  
Vol 487 (4) ◽  
pp. 5346-5362 ◽  
Author(s):  
Suk Sien Tie ◽  
David H Weinberg ◽  
Paul Martini ◽  
Wei Zhu ◽  
Sébastien Peirani ◽  
...  
Keyword(s):  
Correlation Function ◽  
Large Scale ◽  
Signal To Noise Ratio ◽  
Mass Density ◽  
Three Dimensional ◽  
Mean Free Path ◽  
Density Fluctuations ◽  
Data Sets ◽  
Point Correlation ◽  
Point Correlation Function

ABSTRACT Using the Lyman α (Lyα) Mass Association Scheme, we make theoretical predictions for the three-dimensional three-point correlation function (3PCF) of the Lyα forest at redshift z = 2.3. We bootstrap results from the (100 h−1 Mpc)3 Horizon hydrodynamic simulation to a (1 h−1 Gpc)3N-body simulation, considering both a uniform ultraviolet background (UVB) and a fluctuating UVB sourced by quasars with a comoving nq ≈ 10−5h3 Mpc−3 placed either in massive haloes or randomly. On scales of 10–30 h−1 Mpc, the flux 3PCF displays hierarchical scaling with the square of the two-point correlation function (2PCF), but with an unusual value of Q ≡ ζ123/(ξ12ξ13 + ξ12ξ23 + ξ13ξ23) ≈ −4.5 that reflects the low bias of the Lyα forest and the anticorrelation between mass density and transmitted flux. For halo-based quasars and an ionizing photon mean free path of λ = 300 h−1 Mpc comoving, UVB fluctuations moderately depress the 2PCF and 3PCF, with cancelling effects on Q. For λ = 100 or 50 h−1 Mpc, UVB fluctuations substantially boost the 2PCF and 3PCF on large scales, shifting the hierarchical ratio to Q ≈ −3. We scale our simulation results to derive rough estimate of the detectability of the 3PCF in current and future observational data sets for the redshift range z = 2.1–2.6. At r = 10 and 20 h−1 Mpc, we predict a signal-to-noise ratio (SNR) of ∼9 and ∼7, respectively, for both Baryon Oscillation Spectroscopic Survey (BOSS) and extended BOSS (eBOSS), and ∼37 and ∼25 for Dark Energy Spectroscopic Instrument (DESI). At r = 40 h−1 Mpc the predicted SNR is lower by a factor of ∼3–5. Measuring the flux 3PCF would provide a novel test of the conventional paradigm of the Lyα forest and help separate the contributions of UVB fluctuations and density fluctuations to Lyα forest clustering, thereby solidifying its foundation as a tool of precision cosmology.

HIERARCHIES IN THE LARGE-SCALE STRUCTURES OF THE UNIVERSE

2006 ◽  
Vol 15 (08) ◽  
pp. 1199-1215
Author(s):  
T. GOLDMAN ◽  
JUAN PÉREZ-MERCADER
Keyword(s):  
Correlation Function ◽  
Large Scale ◽  
Matter Density ◽  
Density Fluctuations ◽  
Mass Hierarchy ◽  
Maximal Correlation ◽  
Order Of Magnitude ◽  
Point Correlation ◽  
Point Correlation Function ◽  
The Universe

We study the common relationships that exist between the various structures in the Universe, and show that a unifying description appears when these are considered as emerging from dynamical critical phenomena characterized by complex exponents in the two-point correlation function of matter density fluctuations. Since gravity drives their formation, structures are more likely to form where there is maximal correlation in the matter density. Applying this simple principle of maximal correlation to the two-point correlation function in a scaling regime with complex exponents leads to a hierarchy of structures where: (1) the structures can be classified according to an integer and (2) there is a common real exponent for the two-point correlation function across the range of structures. This in turn implies the existence of both universal size and mass hierarchy-order relationships. We show that these relationships are in good agreement with observations, and that sizes and masses for the known structures, from Globules in the Interstellar Medium to Clusters of Galaxies, can be classified (essentially to within one order of magnitude out of more than 10 orders of magnitude) in terms of just three constants.

scholarly journals From correlation functions to event shapes in QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Event Shape ◽  
Proof Of Concept ◽  
Yang Mills ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Event Shapes ◽  
A Charge ◽  
Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

scholarly journals A two-point correlation function for Galactic halo stars

2011 ◽  
Vol 417 (3) ◽  
pp. 2206-2215 ◽  
Author(s):  
A. P. Cooper ◽  
S. Cole ◽  
C. S. Frenk ◽  
A. Helmi
Keyword(s):  
Correlation Function ◽  
Galactic Halo ◽  
Halo Stars ◽  
Point Correlation ◽  
Point Correlation Function

scholarly journals TOWARDS THE PROOF OF AGT-W RELATION: TODA 3-POINT FUNCTION AND ${\mathcal W}_{1+\infty}$ ALGEBRA

2013 ◽  
Vol 21 ◽  
pp. 138-139
Author(s):  
SHOTARO SHIBA
Keyword(s):  
Field Theory ◽  
Correlation Function ◽  
Point Function ◽  
Gauge Groups ◽  
Promising Direction ◽  
Quiver Gauge Theory ◽  
Conformal Theory ◽  
Conformal Field ◽  
Point Correlation ◽  
Point Correlation Function

The AGT-W relation is a conjecture of the nontrivial duality between 4-dim quiver gauge theory and 2-dim conformal field theory. We verify a part of this conjecture for all the cases of quiver gauge groups by studying on the property of 3-point correlation function of conformal theory. We also mention the relation to [Formula: see text] algebra as one of the promising direction towards the proof of the remaining part.

scholarly journals A general treatment of snow microstructure exemplified by an improved relation for the thermal conductivity

2012 ◽  
Vol 6 (6) ◽  
pp. 4673-4693 ◽  
Author(s):  
H. Löwe ◽  
F. Riche ◽  
M. Schneebeli
Keyword(s):  
Thermal Conductivity ◽  
Correlation Function ◽  
Pore Space ◽  
Anisotropy Parameter ◽  
Micro Computed Tomography ◽  
Data Set ◽  
Microstructural Parameters ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Snow Microstructure

Abstract. Finding relevant microstructural parameters beyond the density is a longstanding problem which hinders the formulation of accurate parametrizations of physical properties of snow. Towards a remedy we address the effective thermal conductivity tensor of snow via known anisotropic, second-order bounds. The bound provides an explicit expression for the thermal conductivity and predicts the relevance of a microstructural anisotropy parameter Q which is given by an integral over the two-point correlation function and unambiguously defined for arbitrary snow structures. For validation we compiled a comprehensive data set of 167 snow samples. The set comprises individual samples of various snow types and entire time series of metamorphism experiments under isothermal and temperature gradient conditions. All samples were digitally reconstructed by micro-computed tomography to perform microstructure-based simulations of heat transport. The incorporation of anisotropy via Q considerably reduces the root mean square error over the usual density-based parametrization. The systematic quantification of anisotropy via the two-point correlation function suggests a generalizable route to incorporate microstructure into snowpack models. We indicate the inter-relation of the conductivity to other properties and outline a potential impact of Q on dielectric constant, permeability and adsorption rate of diffusing species in the pore space.

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