Showing papers on "Correlation function (statistical mechanics) published in 1986"
TL;DR: In this article, a spectral correlation theory for cyclostationary time series is introduced, and the spectral correlation properties of Rice's representation for bandpass time-series are derived.
252 citations
TL;DR: The maximum entropy method (MEM) is used to analyze quasielastic light scattering correlation functions as discussed by the authors, and the success of the method is illustrated with results from computer generated noisy data and experimental data from colloidal dispersions.
Abstract: The maximum entropy method (MEM) is used to analyze quasielastic light scattering correlation functions. The central problem, in such data analysis, is the recovery of the distribution of exponentials describing the decay of the correlation function (i.e., inverting the Laplace transform). MEM is shown to give a high‐quality reconstruction of these distributions. The success of the method is illustrated with results from computer‐generated ‘‘noisy’’ data and with experimental data from colloidal dispersions. Both the theoretical properties, and practical advantages of MEM are presented and compared with current data analysis techniques.
130 citations
TL;DR: In this article, the analogies between incoherent quasielastic neutron scattering and deuteron spin alignment in studying single particle reorientations are pointed out, based on the fact that geometrical information is obtained in both methods by manipulation of an appropriate phase factor.
Abstract: The analogies between incoherent quasielastic neutron scattering and deuteron spin alignment in studying single particle reorientations are pointed out. Quasielastic neutron scattering measures the full van Hove correlation function for correlation times shorter than 10−8 s. Spin alignment represents an orientational single particle function for correlation times longer than 10−4 s. The analogy is based on the fact that geometrical information is obtained in both methods by manipulation of an appropriate phase factor. In neutron scattering this phase factor is Q⋅a in momentum space, where Q is the momentum transfer and a is a jump length. In spin alignment the phase factor is δQ⋅τ1 in time space where δQ specifies the strength of the quadrupole coupling and τ1 is a pulse spacing defining the evolution period. It is shown that the measurements of the elastic incoherent structure factor as a function of Q⋅R and the spin alignment echo height as a function of δQ⋅τ1, respectively, yields largely equivalent in...
121 citations
69 citations
TL;DR: In this paper, the authors generalize the model of the nucleation-and-growth process studied by Kolmogorov, Johnson, Mehl and Avrami and derive the exact space-time correlation functions of the two-phase structure which consist of metastable phase and stable phase.
Abstract: We generalize the model of the nucleation-and-growth process studied by Kolmogorov, Johnson, Mehl and Avrami. We then derive the exact space-time correlation functions of the two-phase structure which consist of metastable phase and stable phase. The result includes the case in which the nucleation rate and/or the growth velocity is a function of space and time. Some aspects of these correlation functions are discussed such as the interpretation of their long-time behavior and the relation between the two-point correlation function and elastic scattering scattering.
64 citations
TL;DR: In this paper, the dissipative one-field drift wave equation is solved using the pseudospectral method to generate steady-state fluctuations, analyzed in terms of space-time correlation functions and modal probability distributions.
Abstract: The dissipative one-field drift wave equation is solved using the pseudospectral method to generate steady-state fluctuations. The fluctuations are analyzed in terms of space-time correlation functions and modal probability distributions. Nearly Gaussian statistics and exponential decay of the two-time correlation functions occur in the presence of electron dissipation, while in the absence of electron dissipation long-lived vortical structures occur. Formulas from renormalized, Markovianized statistical turbulence theory are given in a local approximation to interpret the dissipative turbulence.
60 citations
TL;DR: In this article, a general series expansion of arbitrary accuracy is given for the correlation function of the biased regions of galaxy formation in terms of the mass autocorrelations, and the validity of various approximations is discussed.
Abstract: A general series expansion of arbitrary accuracy is given for the correlation function of the 'biased' regions of galaxy formation in terms of the mass autocorrelations. It is shown how to calculate the N-point correlations to arbitrary accuracy, and the validity of the various approximations is discussed. The asymptotic values of the N-point correlation functions at their highest point at zero spatial separation are given, and the scaling of these values is discussed.
59 citations
TL;DR: In this article, the optimal determination of three-body correlation factors is studied within the framework of the variational theory for strongly interacting Bose liquids, where the Euler-Lagrange equation for the three body correlations suggests an iterative procedure in which the threebody correlation factor is expressed as a series of diagrams containing only the pair distribution function.
Abstract: Within the framework of the variational theory for strongly interacting Bose liquids, we study the optimal determination of three-body correlation factors. The Euler-Lagrange equation for the three-body correlations suggests an iterative procedure in which the three-body correlation factor is expressed as a series of diagrams containing only the pair distribution function. The long-wavelength behavior of the three-body structure function agrees formally with the prediction of quantum hydrodynamics. The simplest approximation for the optimized three-body correlation function is identical to the prediction of second-order correlated-basis-function perturbation theory. We show that this simplest approximation sums essentially the same sets of diagrams that are included in non-optimized hypernetted-chain calculations with three-body correlations. Along with the three-body correlations we include those elementary diagrams of fourth and fifth order which have a comparable topological structure. The predictions for the ground-state energy and the pair distribution function are substantially improved compared with hypernetted-chain calculations restricted to two-body correlations.
55 citations
TL;DR: In this article, a renormalisation group study for the long time behavior of a diffusive system with a single conserved density which is subjected to an external driving force is presented. And the exact scaling form of the density correlation function is obtained, and the corresponding universal amplitude agrees excellently with a recent Monte Carlo simulation.
Abstract: We present a renormalisation group study for the long time behaviour of a diffusive system with a single conserved density which is subjected to an external driving force. In the asymptotic long wavelength limit the system approaches an infrared stable fixed point where detailed balance is satisfied. We obtain the exact scaling form of the density correlation function. In one dimension, the corresponding universal amplitude agrees excellently with a recent Monte Carlo simulation.
54 citations
TL;DR: In this article, a detailed study of forecast-error statistics for the operational Canadian large-scale forecast model was made in preparation for reparameterization of the correlation function used in the data assimilation step of the forecast cycle.
Abstract: A detailed study of hemispheric forecast-error (f.e.) statistics for the operational Canadian large-scale forecast model was made in preparation for reparameterization of the correlation function used in the data assimilation step of the forecast cycle. The choice of an appropriate function type for geopotential height and temperature f.e. lag-correlation representations was a major concern. A number of possible functional representations, both isotropic and anisotropic, were considered, and the goodness-of-fit of the various candidate functions to correlations computed from observed f.e. data were compared. The following special form of the second-order autoregressive function was adopted as the function of choice: (1 + c|s|)e−c|s|, where |s| is geographic location separation. An examination of f.e. correlation structure on a regional basis revealed large differences from region to region. Latitudinal, pressure-level, and seasonal dependencies of the statistical structure of constant pressure-su...
52 citations
Journal Article•
TL;DR: In this paper, the authors present a program de calculi cation which permits d'ajuster des parametres lorsque la fonction de correlation a plusieurs variables est lineaire ou non.
Abstract: Presentation d'un programme de calcul qui permet d'ajuster des parametres lorsque la fonction de correlation a plusieurs variables est lineaire ou non. Application a l'evolution de la temperature dans un cylindre
TL;DR: In this paper, a molecular dynamics simulation of liquid CS2 was carried out using site-site Lennard-Jones potentials and the total interaction-induced dipole correlation function was calculated by analysing the intermolecular interactions in self and cross terms as well as in different many-body correlation functions.
Abstract: A molecular dynamics simulation of liquid CS2 was carried out using site-site Lennard-Jones potentials. The total interaction-induced dipole correlation function was calculated by analysing the intermolecular interactions in self and cross terms as well as in different many-body correlation functions. The calculated correlation functions display large static and dynamic cancellation effects showing that a careful study of the various individual correlation functions is a necessary prerequisite for the understanding of the molecular dynamics of liquids. The present data display not perfect, but improved agreement with experimental far infrared absorption spectra as compared to previous simulations.
TL;DR: In this paper, the cross correlation of scattered light intensity by doing experiments on well-defined colloidal systems was studied and the results were in agreement with theoretical predictions: multiple scattering does not contaminate the experimental cross intensity correlation function, whereas the experimental auto-intensity correlation function which contains higher order scattering effects, does not give unambiguous results.
Abstract: We have studied the cross correlation of scattered light intensity by doing experiments on well‐defined colloidal systems The results are in agreement with theoretical predictions: multiple scattering does not contaminate the experimental cross‐intensity correlation function, whereas the experimental auto‐intensity correlation function, which contains higher order scattering effects, does not give unambiguous results
TL;DR: In this paper, the authors measured the normalized correlation function R(f) connecting the signals at the left and right ears in a reverberant room as a function of frequency and found that the dominant effect of head diffraction is to lower the decoupling frequency to 500 Hz, about half the no-head value.
Abstract: The normalized correlation function R( f ) connecting the signals at the left and right ears was measured in a reverberant room as a function of frequency. Head diffraction effects are made evident by comparing these data to the correlation function predicted and observed for two microphones separated by a headwidth (15 cm) of space and moving in the same room. In contrast to the familiar two‐mike sinc(δ) correlation (δ=kd), head diffraction gives a two‐ear correlation function which is well described by sinc(αδ)/[1+(βδ)4]1/2, where α=2.2 and β=0.5. The dominant effect of head diffraction is to lower fD, the decoupling frequency [first zero of R( f )] to 500 Hz, about half the no‐head value. The denominator in the fitted correlation function represents the near total independence of the signals at the two ears above fD. Thus with head diffraction the variance in a paired‐mike room averaged pressure amplitude estimate at around 500 Hz is already as small as that obtained sans head only at frequencies abo...
TL;DR: In this paper, the three particle correlation functions of local atomic distribution at metal ion sites in solutions have been extracted from XANES (X-ray absorption near edge structure) spectra of [CrO4]2− and [MnO4]- ions measured by using synchrotron radiation.
TL;DR: In this article, the changes in thermodynamic derivatives at the glass transition are expressed in terms of correlation functions of the frozen out microscopic pressure and energy fluctuations, and the results for the discontinuities as well as the Prigogine-Defay ratio are obtained within a simple model and agree quite well with experimental results.
Abstract: Based on a microscopic approach we present results for the changes in thermodynamic derivatives at the glass transition. These changes are expressed in terms of correlation functions of the frozen out microscopic pressure and energy fluctuations. Quantitative results for the discontinuities as well as the Prigogine–Defay ratio are obtained within a simple model and agrees quite well with experimental results. A generalized order parameter is identified in terms of a correlation function, describing the frozen in local structure of the glass.
TL;DR: In this article, a microscopic correlation function expression for the signal in four-wave mixing is developed and conditions under which the correlation function may be factorized into a product of two four-point, single-particle correlation functions are specified.
Abstract: A microscopic correlation function expression for the signal in four-wave mixing is developed. Both stationary and transient (i.e., photon-echo) experiments with coherent or incoherent radiation fields are considered. In general, these observables are described by an eight-point correlation function of the dipole operator involving two particles, and the signal cannot be written as an amplitude squared. Conditions under which the correlation function may be factorized into a product of two four-point, single-particle correlation functions are specified. In this case the conventional approach, based on calculating a nonlinear polarization and substituting it as a source in Maxwell's equations, is justified. However, in the presence of long-range spatial correlations in the sample (e.g., near critical points) the conventional formulation breaks down and the present theory should be used.
TL;DR: In this paper, the three-pulse sequence of the two-dimensional NMR experiment studying spin exchange in solids can be analysed easily in the time domain for 13 C spectra governed by one chemical shift tensor.
TL;DR: In this article, the effect of finite resolution on the correlation functions for round and rectangular probeholes, taking the finite resolution of the field emission microscope into account, are derived and discussed, and it is shown that the importance of resolution decreases linearly with increasing emitter radius.
TL;DR: In this article, a renormalization-group treatment of the electron density-density correlation function in a disordered system near the mobility edge is given, and the scaling behavior of the diffusion constant and conductivity in the critical region is determined.
Abstract: We give a full renormalization-group treatment of the electron density-density correlation function in a disordered system near the mobility edge. We extract the scaling behavior of the diffusion constant and conductivity in the critical region. Thus, the behavior of these quantities as a function of wave number and frequency is determined and the crossover between the high-frequency and large-wave-number domains is given explicitly.
TL;DR: In this article, the pair correlation function and the velocity autocorrelation function of screened-Coulomb colloidal liquids, interacting via the Derjaguin-Landau-Verweg-Overbeek potential, are calculated using molecular dynamics.
Abstract: The pair correlation function and the velocity autocorrelation function of screened-Coulomb colloidal liquids, interacting via the Derjaguin-Landau-Verweg-Overbeek potential, are calculated using molecular dynamics. Examination of the structure reveals liquidlike behavior even at the lowest density which corresponds to a volume fraction less than ${10}^{\ensuremath{-}4}$. The calculated radial distribution functions are in excellent agreement with experiment. The velocity autocorrelation function exhibits distinct oscillations at all densities, which indicates that the motion of a single particle is very strongly coupled to the collective modes of the screened-Coulomb colloidal liquid.
TL;DR: In this article, the structure factors of liquid Zn at 450°C and liquid Pb at 340°C have been determined by neutron diffraction with sufficient accuracy and are compared with those by X-ray diffraction.
Abstract: The structure factors of liquid Zn at 450°C and liquid Pb at 340°C have been determined by neutron diffraction with sufficient accuracy and are compared with those by X-ray diffraction. A remarkable difference in these structure factors is clearly found around the first peak region, as well as a slight variation of the first peak position and it is apparently larger than the experimental errors, for both liquid metals. The ion-electron correlation function has been evaluated from this difference with the help of theoretical calculation of the electron-electron correlation function. By the Fourier transform of this function, the radial distribution function of valence electrons around ion has also been calculated. The ionic radii obtained in this work were equivalent to those proposed by Pauling.
TL;DR: In this article, two effective field treatments are presented for the diluted transverse Ising model, which include the effects of correlation, and the critical temperature, the longitudinal and transverse magnetisations, the initial transverse susceptibility and the two-site spin correlation function are calculated for a square lattice.
Abstract: Two effective-field treatments are presented for the diluted transverse Ising model. The methods include the effects of correlation. The critical temperature, the longitudinal and transverse magnetisations, the initial transverse susceptibility and the two-site spin correlation function are calculated for a square lattice. It was found that, in particular, the transverse magnetisation and the initial transverse susceptibility exhibit behaviour which is interesting in the diluted case.
TL;DR: In this paper, the S x S x correlation function of S = 1/2 XXZ chain is numericaly obtained at low temperatures by means of the transfer matrix with use of the Trotter approximation.
Abstract: The S x S x correlation function of S =1/2 XXZ chain is numericaly obtained at low temperatures by means of the transfer matrix with use of the Trotter approximation. The inplane susceptibility and the correlation length are extrapolated to N =∞ where N is the number of the Trotter slicings. It is shown that the extrapolation works quite effectively and makes the estimation of the critical indices ν, γ and η possible for the anisotropy parameter -0.75≤Δ≤0.5. The obtained values of ν, γ and η satisfy the scaling relation and agree quite well with the analytic expression derived by Luther and Peschel.
TL;DR: A closed form approximation to the clipped correlation function valid for arbitrary clipping thresholds is presented and is used to make correlation measurements on speckle from a rotating diffuser using a 2-D random access detector array.
Abstract: Clipped laser speckle is used to measure the correlation of time-varying laser speckle. As with standard intensity correlation, clipped speckle is correlated to determine the magnitude of the correlation coefficient. The simple nature of clipped speckle permits high-speed measurements of correlation and velocity. A closed form approximation to the clipped correlation function valid for arbitrary clipping thresholds is presented. The approximation is used to make correlation measurements on speckle from a rotating diffuser using a 2-D random access detector array.
TL;DR: In this paper, the resistivity fluctuation correlation function and electrostatic potential spectrum of resistivity-gradient-driven turbulence are calculated analytically and compared to the results of three-dimensional numerical calculations.
Abstract: The resistivity fluctuation correlation function and electrostatic potential spectrum of resistivity‐gradient‐driven turbulence are calculated analytically and compared to the results of three‐dimensional numerical calculations. Resistivity‐gradient‐driven turbulence is characterized by effective Reynolds’ numbers of order unity. Steady‐state solution of the renormalized spectrum equation yields an electrostatic potential spectrum 〈φ2〉ky ∼k−3.25y . Agreement of the analytically calculated potential spectrum and mean‐square radial velocity with the results of multiple helicity numerical calculations is good. This comparison constitutes a quantitative test of the analytical turbulence theory used. The spectrum of magnetic fluctuations is also calculated and agrees well with that obtained from the numerical computations.
TL;DR: In this article, the S x - S x correlation function of S = 1 XXZ chain is calculated at low temperatures by means of the transfer matrix with use of the Trotter formula.
Abstract: The S x - S x correlation function of S =1 XXZ chain is calculated at low temperatures by means of the transfer matrix with use of the Trotter formula. Critical properties of the correlation function, such as critical indices γ, η and ν and the mass identified by the inverse correlation length at T =0, are obtained. We conclude that a groundstate with an excitation gap appears for the anisotropy parameter Δ<Δ 1 ≃ -0.3 including the isotropic antiferromagnetic point (Δ=-1). We have obtained η≃1/4 at Δ=Δ 1 in accord with the theoretical prediction by Haldane and den Nijs. Our result, however, shows the monotonic increase of the excitation gap with decreasing Δ for Δ<Δ 1 contrary to Haldane's prediction.
TL;DR: In this article, a graph theoretic analysis is made of the m-spin correlation functions of the lambda-state Potts model, and the correlation functions for m=2 were expressed in terms of rooted mod- lambda flow polynomials.
Abstract: For pt.I see ibid. vol.19 p.411 (1985). A graph theoretic analysis is made of the m-spin correlation functions of the lambda -state Potts model. In paper I, the correlation functions for m=2 were expressed in terms of rooted mod- lambda flow polynomials. The authors introduce a more general type of polynomial, the partitioned m-rooted flow polynomial, which plays a fundamental role in the calculation of the multispin correlation functions. The m-rooted equivalent transmissivities of Tsallis and Levy (1981) are interpreted in terms of percolation theory and are expressed as linear combinations of the above correlation functions.
TL;DR: In this paper, the structure factors of liquid Ga at 50°C and liquid Tl at 315°C have been determined by neutron diffraction with sufficient accuracy and are compared with those by X-ray diffraction.
Abstract: The structure factors of liquid Ga at 50°C and liquid Tl at 315°C have been determined by neutron diffraction with sufficient accuracy and are compared with those by X-ray diffraction. A remarkable difference in these structure factors is clearly found around the first peak region, as well as a slight variation of the first peak position and it is apparently larger than the experimental errors, for both liquid metals. The ion-electron correlation function has been evaluated from this difference with the help of theoretical calculation of the electron-electron correlation function. By the Fourier transform of this function, the radial distribution function of valence electrons around ion has been calculated. The difference of electron distribution between the same valent IIIb-metals are also discussed.
TL;DR: The correlation functions which are suitable for the delocalized interface are defined and evaluated exactly in the two-dimensional solid-on-solid model and the appropriately defined intrinsic pair-correlation function was of the form P(x,y)-x '~ as x~ oo, where x is a distance in the transverse direction.
Abstract: The correlation functions which are suitable for the delocalized interface are defined and evaluated exactly in the two-dimensional solid-on-solid model. The appropriately defined inverse correlation function, which may be a counterpart of the Ornstein-Zernike correlation function for the delocalized interface, is strictly short ranged in the transverse direction and decays exponentially with the new correlation length, independent of system size, in the longitudinal direction. In a system of length L in the transverse direction the quasiroughening transition takes place at temperature ${T}_{r}$ depending on L.