2-Point correlation function of nanostructured materials via the grey-tone correlation function of electron tomograms: A three-dimensional structural analysis of ordered mesoporous silica

2010 ◽  
Vol 58 (3) ◽  
pp. 770-780 ◽  
Author(s):  
Cedric J. Gommes ◽  
Heiner Friedrich ◽  
Petra E. de Jongh ◽  
Krijn P. de Jong
Keyword(s):  
Correlation Function ◽  
Structural Analysis ◽  
Mesoporous Silica ◽  
Nanostructured Materials ◽  
Three Dimensional ◽  
Ordered Mesoporous Silica ◽  
Ordered Mesoporous ◽  
Grey Tone ◽  
Point Correlation ◽  
Point Correlation Function

scholarly journals Photometric Calibration and Large-Scale Clustering in the Universe

1994 ◽  
Vol 161 ◽  
pp. 295-300
Author(s):  
R. Fong ◽  
N. Metcalfe ◽  
T. Shanks
Keyword(s):  
Correlation Function ◽  
Large Scale ◽  
Three Dimensional ◽  
High Signal ◽  
Galaxy Surveys ◽  
Photometric Calibration ◽  
Peculiar Velocities ◽  
Redshift Surveys ◽  
Point Correlation ◽  
Point Correlation Function

The machine measurements of UK Schmidt plates have produced two very large galaxy surveys, the APM survey and the Edinburgh-Durham Southern Galaxy Catalogue (or COSMOS survey). These surveys can constrain the power on large scales of ≳ 10h −1 Mpc better than current redshift surveys, simply because such large numbers, ≳ 2 million galaxies to bJ ≤ 20.5, provide very high signal/noise in the estimated two-point correlation function for galaxies. Furthermore, the results for the three-dimensional galaxy two point correlation function, ξ(r), obtained from the measured projected function, ω(θ), should be quite robust for reasonable model number-redshift distributions, N(z), for these magnitude limits (see, e.g., Roche et al. 1993). Another clear advantage of measuring ω(θ) is that it is unaffected by the peculiar velocities of the galaxies, whereas they have an important effect on the corresponding ξ,(s) using galaxy redshift surveys.

scholarly journals CORRELATION FUNCTIONS OF A CONFORMAL FIELD THEORY IN THREE DIMENSIONS

1996 ◽  
Vol 11 (13) ◽  
pp. 1047-1059 ◽  
Author(s):  
S. GURUSWAMY ◽  
P. VITALE
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Correlation Functions ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Radius Of Curvature ◽  
Nonlinear Sigma Model ◽  
Long Distance ◽  
Point Correlation ◽  
Point Correlation Function

We derive explicit forms of the two-point correlation functions of the O(N) nonlinear sigma model at the critical point, in the large-N limit, on various three-dimensional manifolds of constant curvature. The two-point correlation function, G(x, y), is the only n-point correlation function which survives in this limit. We analyze the short distance and long distance behaviors of G(x, y). It is shown that G(x, y) decays exponentially with the Riemannian distance on the spaces R2×S1, S1×S1×R, S2×R, H2×R. The decay on R3 is of course a power law. We show that the scale for the correlation length is given by the geometry of the space and therefore the long distance behavior of the critical correlation function is not necessarily a power law even though the manifold is of infinite extent in all directions; this is the case of the hyperbolic space where the radius of curvature plays the role of a scale parameter. We also verify that the scalar field in this theory is a primary field with weight [Formula: see text]; we illustrate this using the example of the manifold S2×R whose metric is conformally equivalent to that of R3–{0} up to a reparametrization.

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.

scholarly journals Galaxy Clustering to B = 27M

1994 ◽  
Vol 161 ◽  
pp. 635-643
Author(s):  
N. Roche ◽  
T. Shanks ◽  
N. Metcalfe ◽  
R. Fong
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Redshift Distribution ◽  
Galaxy Clustering ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Luminosity Evolution

The angular two-point correlation function, ω(θ), for galaxies can be used as a probe of their redshift distribution N(z) and, therefore, of galaxy luminosity evolution. Without redshift data, we can still observe the projection onto the two-dimensional sky of the three-dimensional clustering of galaxies. The autocorrelation of this projected distribution is described by ω(θ). Observations have indicated that ω(θ) follows a θ−0.8 power-law (Peebles 1980) and that the index of the power-law remains approximately constant to the faintest limits of photographic surveys (Jones, Shanks & Fong 1987).

scholarly journals Vertically Ordered Mesoporous Silica-Nanochannel Film-Equipped Three-Dimensional Macroporous Graphene as Sensitive Electrochemiluminescence Platform

2021 ◽  
Vol 9 ◽  
Author(s):  
Jiawei Gong ◽  
Hongliang Tang ◽  
Xuan Luo ◽  
Huaxu Zhou ◽  
Xueting Lin ◽  
...  
Keyword(s):  
Mesoporous Silica ◽  
Self Assembly ◽  
Limit Of Detection ◽  
Three Dimensional ◽  
High Sensitivity ◽  
Ordered Mesoporous Silica ◽  
3D Graphene ◽  
Quenching Effect ◽  
Sensing Platform ◽  
Ordered Mesoporous

Three-dimensional (3D) electrochemiluminescence (ECL) platform with high sensitivity and good anti-fouling is highly desirable for direct and sensitive analysis of complex samples. Herein, a novel ECL-sensing platform is demonstrated based on the equipment of vertically ordered mesoporous silica-nanochannel films (VMSF) on monolithic and macroporous 3D graphene (3DG). Through electrografting of 3-aminopropyltriethoxysilane (APTES) onto 3DG as molecular glue, VMSF grown by electrochemically assisted self-assembly (EASA) method fully covers 3DG surface and displays high stability. The developed VMSF/APTES/3DG sensor exhibits highly sensitized ECL response of tris(2,2′-bipyridyl) ruthenium (Ru (bpy)32+) taking advantages of the unique characteristics of 3DG (high active area and conductivity) and VMSF nanochannels (strong electrostatic enrichment). The VMSF/APTES/3DG sensor is applied to sensitively detect an important environmental pollutant (4-chlorophenol, with limit of detection or LOD of 30.3 nM) in term of its quenching effect (ECL signal-off mode) toward ECL of Ru (bpy)32+/tri-n-propylamine (TPrA). The VMSF/APTES/3DG sensor can also sensitively detect the most effective antihistamines chlorpheniramine (with LOD of 430 nM) using ECL signal-on mode because it acts as co-reactant to promote the ECL of Ru (bpy)32+. Combined with the excellent antifouling ability of VMSF, the sensor can also realize the analysis of actual environmental (lake water) and pharmaceutical (pharmacy tablet) samples. The proposed 3D ECL sensor may open new avenues to develop highly sensitive ECL-sensing platform.

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