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Topic: Correlation functions

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Correlation function (astronomy)

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	Correlation function (quantum field theory) - Wikipedia, the free encyclopedia
		In quantum field theory, correlation functions generalize the concept of correlation functions in statistics.
		Depending on n (the number of inserted operators), the correlation functions are called one-point function (tadpole), two-point function, and so on.
		Sometimes, the phrase Green's function is used not only for two-point functions, but for any correlators.
	en.wikipedia.org /wiki/Correlation_function_(quantum_field_theory) (130 words)

	World Intellectual Property Organization (Site not responding. Last check: 2007-10-06)
		The peak of the circular cross-correlation function is located, and an estimate of the frequency shift parameter is derived from the location of the peak of the circular cross- correlation function.
		Figure 5 is a one-dimensional correlation function derived from a cross- section of the two-dimensional correlation function of Figure 3, and representing the likelihood of various Doppler frequency hypotheses.
		The system of claim 13 wherein the logic is configured to circularly cross- correlate the first and second combined correlation functions to form a circular cross- correlation function, locate a peak of the circular cross-correlation function, and derive the estimate of the frequency shift parameter from the location of the peak.
	www.wipo.int /ipdl/IPDL-CIMAGES/view/pct/getbykey5?KEY=05/18087.050224&ELEMENT_SET=DECL (5981 words)

	Democritus: Correlation Functions (Site not responding. Last check: 2007-10-06)
		The best known example of a correlation function is the velocity autocorrelation function, which correlates the velocity of an atom with itself (hence the term autocorrelation).
		The correlation function therefore reveals the time scale for changes in the atomic motion, revealing, for example, the average time between atom-atom collisions.
		Calculating correlation functions in a molecular dynamics simulation is a tricky procedure, but can be thought of as a form of ensemble average.
	www.cse.clrc.ac.uk /msi/software/Democritus/Theory/corfun1.html (418 words)

	Article - Ryan (Site not responding. Last check: 2007-10-06)
		Correlation functions are extremely valuable tools in the interpretation of one dimensional SAXS patterns, particularly those for which features are either weak or obscured (for example shoulders).
		However, the correlation function is affected by the Guinier back-extrapolation to the greatest extent at large values of r, and so the back-extrapolation only has a small effect on the analysis.
		The lower the truncation point is, the rougher the correlation functions, while the higher the truncation point is, the slower the transform.
	www.dl.ac.uk /SRS/CCP13/newsletter94/corfunc.html (2150 words)

	Introduction to DSP - Time domain processing: Correlation functions (Site not responding. Last check: 2007-10-06)
		The correlation function shows how similar two signals are, and for how long they remain similar when one is shifted with respect to the other.
		Even a shift of one sample either way means there is no correlation at all, so the correlation function of random noise with itself is a single sharp spike at shift zero.
		The autocorrelation function of a periodic signal is itself a periodic signal, with a period the same as that of the original signal.
	www.bores.com /courses/intro/time/2_func.htm (195 words)

	Digital images and computer modelling - Correlation functions and bounds
		When computing correlation functions from digital images, it is important to correctly handle certain technical isues such as converting to polar coordinates, especially at small r, and to consider the limitations of digital images, such as digitizing curved surfaces, which were mentioned earlier.
		Other than characterizing pore geometry, one of the principal uses of correlation functions is in the area of computing bounds for the effective properties of composite materials [45,46].
		As bounds incorporate higher and higher correlation functions, they are known to become tighter and tighter, increasing their usefulness at the expense of a great increase of computational difficulty.
	ciks.cbt.nist.gov /garbocz/appendix3/node6.html (1429 words)

	Correlation functions for ionic motion from NMR relaxation and electrical conductivity in the glassy fast-ion conductor ... (Site not responding. Last check: 2007-10-06)
		Correlation functions for ionic motion from NMR relaxation and electrical conductivity in the glassy fast-ion conductor (Li (SiS
		The measured correlation times from the two effects differ by two orders of magnitude, and the derived distributions are shifted greatly relative to each other.
		This correlates the two effects in a simple and effective way; both time- correlation functions can be calculated approximately from the distributions, and even the dc conductivity can be calculated from the NMR results.
	cmp.ameslab.gov /cmp/Abstracts/borsa_14.html (213 words)

	Distribution Functions
		the periodic function of the coordinates, corresponding to the crystal lattice.
		It is customary to define the n-particle correlation function
		SPA assumes, that the correlations between any two molecules are unaffected by the presence of the third one.
	www.plmsc.psu.edu /~www/matsc597c-1997/systems/Lecture3/node2.html (1001 words)

	Information correlation functions
		These are one measure of the degree of mutual dependence of two variables.The order-3 information correlation functions are less amenable to interpretation (see sections 3.13 and 3.14 for interpretations of the information correlation functions), but give an information correlation of three random variables, which is zero iff any two subsets are independent.
		In later chapters we will analyze the information correlation structure of several physical systems and draw conclusions about how the correlation structure indicates underlying physical phenomena.
		Information correlation functions have attracted the attention of liquid theorists [26] and plasma theorists [39, 84].
	www.realtime.net /~drwolf/papers/dissertation/node26.html (199 words)

	Correlation functions - Gaussian model with
		For large r it should fall off to zero (distant points should be uncorrelated); for small r it should be positive (nearby points should be ferromagnetically correlated).
		For h=0, all correlations are zero except for the case q
		The correlation length can play no role, since it must be a solution of the Laplace equation (DH equation with screening length taken to infinity).
	www.uic.edu /classes/phys/phys461/phys532-03/notes/notes10.html (446 words)

	(iv) Correlation functions
		Once the form factors for a particular operator have been determined one is in principle in the position to compute the correlation functions by expanding them in terms of
		Thus, from a practical point of view, with regard to the computation of correlation functions, it is sufficient to determine just the first
		Taking the log of the two-point function there has been a proposal [ 111 ] which could ease the computational task and indeed there has been some recent progress [6 ] along these lines at least for the case of the Ising and sinh-Gordon model.
	www.staff.city.ac.uk /~fring/ResInt/node10.html (247 words)

	Lecture Notes on Dynamic Correlation Functions (Site not responding. Last check: 2007-10-06)
		The Green's function for the diffusion equation is a spreading Gaussian with the mean squared displacement equal to 6 D t.
		If we measure the response to A of a perturbation B it is the correlation between A and the time derivative of B (or vice versa) which enters.
		One of the most important correlations is the auto-correlation function, which is defined as , the time correlation of a function with itself.
	bguy.mse.uiuc.edu /matse485/lnotes/dynamics.html (1057 words)

	Inhomogeneous correlation functions for a planar membrane model neuron (Site not responding. Last check: 2007-10-06)
		The formulation of the electrostatic potentials is via the BBGKY hierarchy for the molecular distribution functions in the civilised model of an electrolyte and is similar to that of Outhwaite's derivation for the primitive model, (J. Chem.
		Though, the usual assumption of bulk electroneutrality is replaced by the macroscopic electroneutrality condition with the inclusion of surface charges.
		The results obtained for the pair correlation functions exhibit a shielding both in the normal and transverse directions.
	www.physics.adelaide.edu.au /mathphysics/abstracts/wje-1.html (179 words)

	correlation functions (Site not responding. Last check: 2007-10-06)
		The two-point correlation function for galaxies is defined as
		The correlation function describes the probability, given one galaxy in a volume dV, of finding a second galaxy in a volume dV at a distance r from the first.
		However, the difference is not significant enough to have to specify luminosity in the correlation function (Peebles 1993).
	astron.berkeley.edu /~kpeek/cosmology/corr_fn_2pt.htm (257 words)

	Determinant representation for dynamical correlation functions of the Quantum nonlinear Schrödinger equation. - ... (Site not responding. Last check: 2007-10-06)
		Determinant representation for dynamical correlation functions of the Quantum nonlinear Schrödinger equation.
		Mori and M. Sato [1] was based on the determinant representation of these correlation functions obtained by A. Lenard [2].
		1 The time-dependent correlation function of an impenetrable B..
	citeseer.ist.psu.edu /kojima96determinant.html (409 words)

	I(2)FROG, JOSAB (Site not responding. Last check: 2007-10-06)
		The correlation function is chirped in these experiments due to deliberate unbalanced dispersion in the interferometer generated by placing a dispersive material (water) in one arm, but not the other.
		FROG trace generated from the correlation function, (c), recovered by application of the algorithm to the data in (a).
		FROG trace generated from the correlation function, (f), recovered by application of the algorithm to the data in (d).
	www.chem.duke.edu /~stimson/frogfolder/i2frog.html (4761 words)

	Analytical Expressions for Correlation Functions and Kirchhoff Integrals for Gaussian Surfaces with Ocean-Like Spectra ...
		Analytical Expressions for Correlation Functions and Kirchhoff Integrals for Gaussian Surfaces with Ocean-Like Spectra
		In this paper, we present closed-form expressions for the correlation functions associated with Gaussian surfaces with certain ocean-like spectra.
		These correlation functions may be used to derive asymptotic expansions for the Kirchhoff integral with a wide range of validity.
	library.wolfram.com /infocenter/Articles/1758 (196 words)

	Statiscal study of turbulence - spectral functions and correlation coefficients (Site not responding. Last check: 2007-10-06)
		Statiscal study of turbulence - spectral functions and correlation coefficients
		An extensive discussion is given of various possible correlation functions for homogeneous and isotropic turbulence.
		The logical consequence of each of several choices of such correlation functions is examined in detail.
	naca.larc.nasa.gov /reports/1958/naca-tm-1436 (62 words)

	Citebase - Point Processes and the Infinite Symmetric Group. Part II: Higher Correlation Functions
		We find an integral representation of all the correlation functions and their explicit expression in terms of multivariate hypergeometric functions.
		Such a form for correlation functions is well known in the random matrix theory and mathematical physics.
		We prove that the correlation functions of the processes are given by determinantal formulas with a certain kernel.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/9804087 (1024 words)

	Correlation Functions
		With the result (192) it is easy to calculate the correlation function of a boson or a fermion field.
		The second factor is equal to the correlation function (192).
		When it comes to calculating the Green functions of the fundamental fields of the original theory, however, only a small portion of this Hilbert space is used.
	www.physik.fu-berlin.de /~kleinert/kleiner_re239/node16.html (767 words)

	115a
		These results are established by relating the correlation functions to a sum over the prime numbers, and at present it is possible to prove a rigorous result only in the range where the ``diagonal terms'' in the sum are dominant.
		Goldston, Gonek, and Montgomery have shown that the pair correlation conjecture is equivalent to a statement about the variation of the distribution of primes.
		It would be a significant accomplishment to prove anything about the correlation functions outside the range in which they currently are known.
	www.aimath.org /WWN/lrmt/articles/html/115a (350 words)

	Information correlation functions
		In these regions at each order lower than the number of spins there is structure having to do with the transitions that cannot be captured by still lower order distributions.
		The ferromagnetic side of the graphs appears far simpler, with almost all of the structure being captured by the lower order distributions (the first order information correlation is the first order negentropy).
		In a single system there are thus two regions where the behavior of the information correlation functions is vastly different, and where the complexity of the description needed is therefore vastly different.
	www.realtime.net /~drwolf/papers/dissertation/node91.html (236 words)

	Citebase - Correlation functions for M^N/S_N orbifolds
		Thus, even though the CFT is defined on the sphere, the correlators are expressed in terms of partition functions on Riemann surfaces with a finite range of genus g.
		For 3-point functions we give an explicit form for the contribution from the sphere, and for the 4-point function we do an example which has genus zero and genus one contributions.
		The condition for the genus zero contribution to the 3-point functions to be non--vanishing is similar to the fusion rules for an SU(2) WZW model.
	citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:hep-th/0006196 (1273 words)

	General properties of time correlation functions (Site not responding. Last check: 2007-10-06)
		A time correlation function may be evaluated as a time average, assuming the system is ergodic.
		An example of a signal and its time correlation function appears in the figure below.
		In this case, the signal is the magnitude of the velocity along the bond of a diatomic molecule interacting with a Lennard-Jones bath.
	www.nyu.edu /classes/tuckerman/stat.mech/lectures/lecture_21/node4.html (208 words)

	[No title]
		FïmGÁ 5?·êøó0ô•ô0ÅôôíøÍêíø0ôÍê hhhhÙLecture 5 : Correlation Functions Delay and Cross-correlation : Let’s remember the definition of Cross-Correlation: We want to know the effect of delaying the functions f and g respectively by a and b on the result of cross-correlation.
		Normalized Correlation Functions: The auto-correlation function and the cross-correlation function can be normalized: The proof for the cross-correlation normalization is given below: Let (be a real number.
		However, as the function in time domain expands horizontally, the Fourier transform in frequency domain not only contracts horizontally but also grows vertically in such a way as to keep constant the area beneath it.
	www.ce.berkeley.edu /Courses/CE286/DigitalDataNotes.doc (1477 words)

	correlation functions (Site not responding. Last check: 2007-10-06)
		The result: a smearing of the correlation in the radial direction--the so-called finger-of-God effect.
		Since galactic superclusters are slowly expanding, galaxies on the near side of superclusters appear closer in redshift space while those on the side appear further away in redshift space.
		The result is a slight flattening of the correlation function at large r.
	astron.berkeley.edu /~kpeek/cosmology/old/fog.htm (222 words)

	General correlation functions (Site not responding. Last check: 2007-10-06)
		Next: The pair correlation function Up: Distribution functions in classical Previous: Distribution functions in classical
		A general correlation function can be defined in terms of the probability distribution function
		Another useful way to write the correlation function is
	www.nyu.edu /classes/tuckerman/stat.mech/lectures/lecture_9/node2.html (64 words)

	Quantitative Comparison of Real and CEMHYD3D Model Microstructures Using Correlation Functions
		In addition to a visual presentation of extracted two-dimensional images, the comparison is based on the calculation of the normalized two-point correlation function for a variety of phases including unhydrated cement, hydration products, and capillary porosity.
		Both the visual and correlation comparisons are favorable, and several interesting observations from the correlation analysis are introduced and discussed.
		This analysis provides one further validation of the use of microstructure models to predict the microstructure and properties of cement-based materials.
	ciks.cbt.nist.gov /~bentz/microcompare (189 words)

	Equilibrium Time Correlation Functions from Irreversible Transformations in Trajectory Space (Site not responding. Last check: 2007-10-06)
		We present a new identity for the statistical mechanics of trajectories, showing that a distribution of irreversible transformations between ensembles of trajectories is sufficient to determine equilibrium time correlation functions.
		We focus on the specific application to population correlation functions characterizing chemical kinetics.
		In this context we use the identity to compute reaction rate constants through appropriate averaging of an effective work to switch from nonreactive to reactive trajectory ensembles.
	pubs.acs.org /cgi-bin/abstract.cgi/jpcbfk/2004/108/i21/abs/jp037211l.html (179 words)

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