Showing papers on "Correlation function (statistical mechanics) published in 1989"
TL;DR: In this article, the authors describe how the true statistical error on an average of correlated data can be obtained with ease and efficiency by a renormalization group method, illustrated with numerical and analytical examples, having finite as well as infinite range correlations.
Abstract: We describe how the true statistical error on an average of correlated data can be obtained with ease and efficiency by a renormalization group method. The method is illustrated with numerical and analytical examples, having finite as well as infinite range correlations.
678 citations
TL;DR: In this article, the authors consider dynamic light scattering by non-ergodic media, such as glasses or gels, in which the scattering elements are able only to make limited Brownian excursions about fixed average positions.
Abstract: We consider dynamic light scattering (DLS) by non-ergodic media, such as glasses or gels, in which the scattering elements are able only to make limited Brownian excursions about fixed average positions. We point out that, for such media, the time-averaged correlation function of the intensity of scattered light, the quantity obtained from a single DLS measurement, is different from the ensemble-averaged function. An expression for this time-averaged intensity correlation function is derived and its properties and experimental analysis are discussed. Some of the literature on DLS by polymer gels is re-evaluated in the light of these new theoretical predictions.
510 citations
TL;DR: In this paper, a general phase diagram for isotropic antiferromagnetic chains has been proposed using conformal field theory, which is further used to predict the spectrum of finite chains, including logarithmic corrections.
Abstract: A general phase diagram for isotropic antiferromagnetic chains has been proposed recently, using conformal field theory. This is developed further to predict the spectrum of finite chains, including logarithmic corrections. These predictions are tested against Bethe ansatz and exact diagonalisation results for various Hamiltonians with s=1/2, 1 and 3/2. Logarithmic corrections to correlation functions and the scaling of gaps for infinite systems are also given.
285 citations
TL;DR: In this paper, the authors make use of a numerical method for generating random rough surfaces to study the effects of sampling interval on measured surface correlation functions, and they conclude that the sampling interval must be at least as small as one tenth of the surface correlation length, for these high-frequency variations to be recorded and hence for the inherent exponential nature of a surface to be measured.
Abstract: The authors make use of a numerical method for generating random rough surfaces to study the effects of sampling interval on measured surface correlation functions. This numerical investigation avoids some of the complications present in experimental studies of the effects of this parameter, such as instrument resolution and measurement reproducibility. The numerical technique is used to generate surfaces with exponential correlation functions and surfaces with gaussian correlations. The short-wavelength fluctuations on the exponential surfaces are clearly seen, these arising from the high-frequency tail in the surface power spectrum. The authors are able to quantify the sampling interval necessary to record this short-range surface behaviour. They conclude that the sampling interval must be at least as small as one tenth of the surface correlation length, for these high-frequency variations to be recorded and hence for the inherent exponential nature of the surface to be measured.
130 citations
TL;DR: In this article, a new set of equations has been derived that governs the dynamics of the inhomogeneous background plasma and the superimposed incompressible fluctuations in the solar-wind plasma and their radial evolution into interplanetary space.
Abstract: On the basis of the ideal MHD equations expressed in terms of Elsasser variables, a new set of equations has been derived that governs the dynamics of the inhomogeneous background plasma and the superimposed incompressible fluctuations. From these equations the dynamic equation for the two-point and two-time correlation tensor has been obtained, and subsequently the equations of motion for the various spectral densities related to energy, cross-helicity and residual energy or the Alfven ratio have been established. This set of equations offers a new possibility of discussing and perhaps better understanding the mostly incompressible fluctuations observed in the solar-wind plasma and of analysing their radial evolution into interplanetary space and their spectral development. The scope of the paper is limited to giving mainly formal developments of the equations. A detailed evaluation of the many terms in the light of interplanetary observations is intended for the future, but is not presented in this paper.
108 citations
TL;DR: Analytic approximations for the third- and higher-order direct correlation functions of uniform classical liquids are presented, derived from a weighted-density approximation for the one-particle direct correlation function of a nonuniform liquid which requires as input only the two-particles function of the corresponding uniform liquid.
Abstract: Analytic approximations for the third- and higher-order direct correlation functions of uniform classical liquids are presented. These are derived from a weighted-density approximation for the one-particle direct correlation function of a nonuniform liquid which requires as input only the two-particle function of the corresponding uniform liquid. The three-particle result is shown to have the same accuracy as two recently proposed approximations, but has a much simpler form. The four- and five-particle results are new, and in principle can be tested by simulation methods.
100 citations
TL;DR: In this article, the damage or Hamming distance between two configurations of Ising spins is investigated and an exact relation between the difference of the two possible types of damage and the spin-spin correlation function is found.
Abstract: We investigate the damage or Hamming distance between two configurations of Ising spins. We find an exact relation between the difference of the two possible types of damage and the spin-spin correlation function, which is generally valid. For the specific case of ferromagnetic interactions, heat bath dynamics and same sequence of random numbers, this relation involves only one type of damage. The susceptibility and the magnetization can also be expressed in terms of the damage. Numerical determination of the damage for the 2d Ising model is not only an efficient way to calculate correlation functions but also gives access to spin fluctuations visualized as clusters of damaged sites which have a fractal dimension d−β/ν at Tc and whose size distribution is also related to static exponents.
90 citations
TL;DR: In this article, the specular component of leaf reflectance comprising the presence of the leaf-wax layer is introduced and the scattering phase function is derived for this case, and the correlation function characterizing the probability that a point inside the canopy or on the soil is seen from two directions is considered.
Abstract: The governing equation for photon transport in plant canopies is discussed. The specular component of leaf reflectance comprising the presence of the leaf-wax layer is introduced. The scattering phase function is derived for this case. By separating the first-order scattering into an independent problem, the leaf size is taken into account in obtaining the hot-spot effect of the canopy. The correlation function characterizing the probability that a point inside the canopy or on the soil is seen from two directions is considered. Numerical results for the transport equation obtained by the method of discrete ordinates are compared with those obtained by using the Monte Carlo method and experimental data.
84 citations
TL;DR: The superfluid transition in a two-dimensional /sup 4/He system has been studied using computational-path-integral methods and the order-parameter correlation function shows an algebraic decay in good agreement with spin-wave theory.
Abstract: The superfluid transition in a two-dimensional /sup 4/He system has been studied using computational-path-integral methods. Thermodynamic and structural properties, the single-particle momentum distribution, the one-particle off-diagonal density matrix (or order-parameter correlation function), the momentum correlations, the superfluid density (based on the winding-number distribution) and the vorticity correlation function were calculated for temperatures above and below the superfluid transition for a film density of 0.0432 A/sup -2/ (which corresponds to zero pressure in the ground state). The order-parameter correlation function shows an algebraic decay in good agreement with spin-wave theory. An indirect estimate based on an analysis of finite-size effects using the Kosterlitz-Thouless recursion relations leads to a vortex diameter of 3.7 +- 0.4 A, a vortex core energy of 2.7 +- 0.2 K and a critical temperature of 0.72 +- 0.02 K.
81 citations
TL;DR: In this article, the exact statistical mechanical solution to the problem of an equilibrium inhomogeneous classical one-dimensional mixture of hard rods is presented, and thermodynamic properties, density profiles, and correlation functions of hard rod fluids confined to small regions (micropores) can be calculated.
Abstract: The exact statistical mechanical solution to the problem of an equilibrium inhomogeneous classical one‐dimensional mixture of hard rods is presented. From the solution, thermodynamic properties, density profiles, and correlation functions of hard rod fluids confined to small regions (micropores) can be calculated. The theory is applied to investigate microstructure, pore pressures, and pore adsorption selectivity of micropores in equilibrium with binary hard rod mixtures. A prescription is suggested for generalizing the one‐dimensional results to higher dimensions.
74 citations
TL;DR: In this paper, the fonctions de correlation obtenues a partir des mesures dielectriques et de diffusion lumineuse (en utilisant the representation de Kohlrausch-Williams-Watts) sont quasi identiques.
Abstract: Mesure au voisinage de Tg (−26 o C) de la perte dielectrique et de la fonction d'autocorrelation de l'intensite et utilisation calcul de la fonction de correlation de reorientation dipole-dipole a l'aide de l'equation de Hauriliak-Negami. Les fonctions de correlation obtenues a partir des mesures dielectriques et de diffusion lumineuse (en utilisant la representation de Kohlrausch-Williams-Watts) sont quasi identiques
TL;DR: The general equivalence between D-dimensional probabilistic cellular automata and (D+1)-dimensional equilibrium spin models satisfying a "disorder condition" is first described in a pedagogical way and then used to analyze the phase diagrams, the critical behavior, and the universality classes of some automata as discussed by the authors.
Abstract: The general equivalence betweenD-dimensional probabilistic cellular automata (PCA) and (D+1)-dimensional equilibrium spin models satisfying a “disorder condition” is first described in a pedagogical way and then used to analyze the phase diagrams, the critical behavior, and the universality classes of some automata. Diagrammatic representations of time-dependent correlation functions of PCA are introduced. Two important classes of PCA are singled out for which these correlation functions simplify: (1) “Quasi-Hamiltonian” automata, which have a current-carrying steady state, and for which some correlation functions are those of aD-dimensional static model. PCA satisfying the detailed balance condition appear as a particular case of these rules for which the current vanishes. (2) “Linear” (and more generally “affine”) PCA for which the diagrammatics reduces to a random walk problem closely related to (D+1)-dimensional directed SAWs: both problems display a critical behavior with mean-field exponents in any dimension. The correlation length and effective velocity of propagation of excitations can be calculated for affine PCA, as is shown on an explicitD=1 example. We conclude with some remarks on nonlinear PCA, for which the diagrammatics is related to reaction-diffusion processes, and which belong in some cases to the universality class of Reggeon field theory.
TL;DR: In this article, a molecular dynamical study of one methane molecule in a cavity of NaA zeolite is performed in order to compare calculated to experimental data obtained by infrared spectroscopy and neutron scattering experiments in the temperature range 300-30 K.
Abstract: A molecular dynamical study of one methane molecule in a cavity of NaA zeolite is performed in order to compare calculated to experimental data obtained by infrared spectroscopy and neutron scattering experiments in the temperature range 300–30 K. The calculation shows the trajectory of the molecule in the cavity and then the occupied volume as a function of energy. It allows the calculation of average quantities and correlation functions: (i) the mean field felt by the molecule comparable to the field responsible for the induced infrared band ν1, (ii) the average of the potential energy (to be compared to the heat of adsorption) and of the velocity squared, (iii) the external frequency distribution, and (iv) the position autocorrelation function which is related to the dynamical structure factor seen by neutron scattering.
TL;DR: In this paper, the ground-state and finite-temperature properties of the one-dimensional isotropic spin-1/2 Heisenberg magnet with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest neighbor interactions are investigated.
Abstract: We study the ground-state and finite-temperature properties of the one-dimensional isotropic spin-1/2 Heisenberg magnet with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions which compete with each other. Extrapolating the exact results for finite-size systems of up to 20 spins, we estimate the ground-state energy and the ground-state two-spin correlation function in the infinite-size limit. Using the cluster transfer matrix method, we also calculate the temperature dependence of the internal energy and the specific heat and that of the inverse correlation length and the wave number, by both of which the asymptotic behavior of the two-spin correlation function in the long-distance limit is characterized. We compare the results of these calculations with those obtained previously for the case where the nearest-neighbor interaction is antiferromagnetic.
TL;DR: In this article, a unified colored noise approximation (UCNA) was proposed for colored Gaussian noise driven nonlinear systems with inertia, which replaces a three-dimensional Markovian process by a reduced, two-dimensional MMD with new drift and diffusion coefficients.
Abstract: We present a novel approximation scheme, termed unified colored noise approximation (UCNA), for colored Gaussian noise driven nonlinear systems with inertia. This approximation allows one to evaluate static (stationary distributions, moments) as well as dynamical quantities (correlation functions) for small-to-moderate-to-large values of the correlation time. The approximation replaces a three-dimensional Markovian process by a reduced, two-dimensional Markovian dynamics with new drift and diffusion coefficients. For a harmonic potential the stationary moments are reproduced exactly. Most importantly, we present a criterion involving the noise strengthD, the friction strength γ and the noise color τ, which describes the region of validity of UCNA in the parameter space given by (D, τ, γ). At small τ-values we contrast the UCNA with the well-known small τ approximation. In order to have a comparison onanalytical grounds, we test the static and dynamical predictions of UCNA versus the well-known analytical results obtained from a three-dimensional Ornstein-Uhlenbeck process.
TL;DR: The reliability of a recently proposed parameterization of the bridge function for hard spheres (1987, Molec. Phys., 60, 663) has been tested for densities near the phase transition as mentioned in this paper.
Abstract: The reliability of a recently proposed parameterization of the bridge function for hard spheres (1987, Molec. Phys., 60, 663) has been tested for densities near the phase transition. We carried out simulations of the radial distribution function at reduced densities of 0·925 and 0·94. The radial distribution function calculated from the parameterized bridge function by means of the Ornstein-Zernike equation is in perfect agreement with the simulated values. A parameterization of the bridge function for separations below contact has been proposed.
TL;DR: A survey of neutron diffraction investigations of the static structure factor S(Q) of liquid rubidium and cesium expanded by heating towards conditions close to their critical points is given in this article.
Abstract: A survey is given of neutron diffraction investigations of the static structure factor S(Q) of liquid rubidium and cesium expanded by heating towards conditions close to their critical points. The data are used to derive the characteristic changes of the microscopic structure—such as the distance and number of nearest neighbours—as a function of density. After a brief discussion of recent measurements of the isothermal density derivative of S(Q) of expanded liquid cesium, which is related to the triplet correlation function, we describe the theoretical attempts which have been undertaken so far to extract information from the structure data about the density dependent changes of the effective interaction potential as the metalnonmetal transition is approached.
TL;DR: In this article, the optical memory effect is studied for transmission and reflection, and two-dimensional scaling of the correlation function is obtained for smooth-surfaced samples from theory and from experiment.
Abstract: Geometric scaling of the optical memory effect is studied for transmission and reflection. Two-dimensional momentum matching, and two-dimensional scaling of the correlation function, is obtained for smooth-surfaced samples from theory and from experiment. Very rough-surfaced samples exhibit three-dimensional scaling. Internal surface reflections are found to play an important role in determining the width of the correlation function, and are shown substantially to account for previous discrepancies between theory and experiment.
TL;DR: In this article, the spherically averaged Fermi-hole correlation function in the Hartree-Fock theory was compared with the corresponding function employed in local density functional theory.
Abstract: We have compared, for atomic systems, the spherically averaged Fermi-hole correlation function in the Hartree–Fock theory with the corresponding function employed in local density functional theory. It is shown that, in contrast to , the function behaves qualitatively incorrectly at positions r1 of the reference electron far from the nucleus. Furthermore, we have shown that the qualitatively incorrect behaviour of can be remedied by an approximate expansion of in powers of s, where s is the inter-electronic distance. However, such an expansion must be conducted in two regions due to the discontinuity of as a function of s at the atomic nucleus. Based on the two-region expansion of we have developed an alternative approximate density functional expansion for the spherically averaged Fermi-hole correlation function. The corresponding exchange energy density functional yields values for the exchange energies of atoms in good agreement with Hartree–Fock results. Keywords: atomic exchange energy, density funct...
TL;DR: In this article, the authors generalized the Feigin-Fuchs construction to the torus and proposed an ansatz for certain correlation functions of the minimal conformal models, which is periodic, modular-covariant and has the correct short-distance behavior.
TL;DR: In this paper, a time-dependent nonphotochemical hole burning linewidth for cresyl violet in ethanol glass is reported from 100 ms to 3000 s at 1.3 K.
TL;DR: In this article, the transverse spatial intensity fluctuations of a wave propagating through a medium with a power-law autocorrelation function of wave speed are modeled over a regime that spans 108 in scattering strength and 106 in scaled range (range divided by the Fresnel length).
Abstract: Ewart and Percival [J. Acoust. Soc. Am. 80, 1745 (1986)] have shown that the generalized gamma distribution effectively models intensity probability distributions of temporal fluctuations observed in a field experiment and transverse spatial fluctuations simulated in numerical experiments. In both cases the fluctuations are due to wave propagation through a medium with a random index of refraction. Here, the transverse spatial intensity fluctuations of a wave propagating through a medium with a power‐law autocorrelation function of wave speed are modeled over a regime that spans 108 in scattering strength and 106 in scaled range (range divided by the Fresnel length). This scattering parameter regime transforms to ranges between 100 m and 100 km and to frequencies between 100 Hz and 100 kHz when normalizations typical of observed ocean internal wave fluctuations are used. Contour plots of the variance, skewness, and kurtosis of the intensity distribution are presented for the range/frequency plane. It is s...
TL;DR: The results suggest that the correlation length in calf liver is less than 100 microns and that a root-mean-square path length variation of about 20 microns results from propagation through a 100-mm calf liver path.
Abstract: An expression based on a perturbation method is employed to estimate the correlation of path length difference in a plane normal to the direction of wave propagation from measurements of ultrasonic scattering by model random media and calf liver. The expression gives the correlation function of path length difference in terms of an integral of the correlation function of the medium variations or an equivalent integral of the power spectrum of medium variations, both for a scattering angle of zero degrees. Power spectra derived from measurements of average differential scattering cross section over a spatial‐frequency window are used to fit analytic functions that extend over all spatial frequencies. The results for the windowed and unwindowed data yield correlation functions and corresponding power spectra that are used to estimate the correlation function of path length difference. The results suggest that the correlation length in calf liver is less than 100 μm and that a root‐mean‐square path length variation of about 20 μm results from propagation through a 100‐mm calf liver path.
TL;DR: A new Monte Carlo sampling technique is used to study the spin-1/2 Heisenberg antiferromagnet and good agreement is found between the calculated and experimental correlation lengths in La/sub 2/CuO/sub 4.
Abstract: A new Monte Carlo sampling technique is used to study the spin-1/2 Heisenberg antiferromagnet on square lattices of up to 256 spins. The energy, specific heat, uniform and staggered susceptibilities, and correlation function are calculated. The correlation length as a function of temperature is deduced from correlation functions and is shown to be consistent with a quantum-renormalized classical approximation. Using the coupling constant provided by Raman scattering experiments, good agreement is found between the calculated and experimental correlation lengths in La/sub 2/CuO/sub 4/.
01 Feb 1989-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this paper, a detection device for light charged particle correlation measurements has been designed, which permits the determination of correlation functions at very small relative momenta, and the angular part of the relative momentsa is precisely determined from information delivered by a multi-wire chamber.
Abstract: A new detection device for light charged particle correlation measurements has been designed. This device permits the determination of correlation functions at very small relative momenta. In addition the angular part of the relative momenta is precisely determined from information delivered by a multiwire chamber. This setup opens new possibilities for the study of the correlation function of light charged particles as illustrated by preliminary results for the reaction system 20Ne+27Al at 30 MeV/nucleon.
TL;DR: The scattering function is calculated in mean field approximation for two different thermodynamic states of a lattice model of oil-water-amphiphile solutions, one a disordered state and the other a one dimensionally ordered (lamellar) state as discussed by the authors.
Abstract: The scattering function is calculated in mean‐field approximation for two different thermodynamic states of a lattice model of oil–water–amphiphile solutions, one a disordered state and the other a one‐dimensionally ordered (lamellar) state. The total scattering function for the former, and the fluctuation contribution to the scattering function for the latter, have maxima near q=1, where q is the magnitude of the scattering vector q in units of the reciprocal lattice spacing. For q up to and a little beyond the maximum the scattering functions and their spherical averages (averaged over the surface of a sphere of radius q in q space) are of the Teubner–Strey form I(q)=I(0)/(1−bq2+cq4) with b and c both positive, as in microemulsions. It implies a correlation function that is an exponentially damped sinusoid, of wavelength d and attenuation length, determined by b and c.
TL;DR: In this article, dead-time effects on measured mean count rates and temporal correlation functions of light with gamma-distributed intensity are corrected by using a general p-type detector model and a new approximation for nonparalyzable systems.
Abstract: Dead-time effects on measured mean count rates and temporal correlation functions of light with gamma-distributed intensity are corrected by using a general p-type detector model and a new approximation for nonparalyzable systems. Successful corrections of simulated and measured correlation functions of light scattered by Brownian particles support the validity of our model calculations.