Showing papers on "Correlation function (statistical mechanics) published in 1980"
TL;DR: In this article, a discussion of the general properties of the one-dimensional electron density correlation function K(z) of a partially crystalline polymer with lamellar structure is presented.
Abstract: A discussion of the general properties of the one-dimensional electron density correlation function K(z) of a partially crystalline polymer with lamellar structure shows that application of a graphical extrapolation procedure permits direct determination of the crystallinity, the specific inner surface, and the electron density difference ηc − ηa The procedure is based upon the occurrence of a straight section in the “self-correlation” range of K(z) Curved and nonparallel lamellae do not invalidate the concept In the case of heterogeneous samples composed of partially crystalline and totally amorphous regions, some of the parameters of the experimentally obtained correlation function, as for example the invariant K(0), are affected and may lose their definiteness Use of the method is demonstrated in a detailed discussion of the correlation functions measured for a sample of lowdensity polyethylene at 25 and 100°C
642 citations
TL;DR: In this article, the Jeener-Broekaert pulse sequence was used to detect deuteron line shapes, from which the orientational distribution of partially ordered solids or solid polymers may be determined.
Abstract: Deuteron spin alignment offers a new possibility to investigate extremely slow rotational motions in solids and solid polymers. A convenient theoretical description of the creation and detection of spin alignment by application of the Jeener–Broekaert pulse sequence is given for both static and slowly time dependent quadrupole coupling, as well as for spin–lattice relaxation of spin alignment. It is shown that the NMR signal following spin alignment yields a correlation function of the time dependent quadrupole coupling. This correlation function is evaluated explicitly for a deuteron on the corner of a regular tetrahedron undergoing tetrahedral jumps. Various applications of deuteron spin alignment are demonstrated experimentally, e.g., its use to obtain undistorted deuteron line shapes, from which the orientational distribution of partially ordered solids or solid polymers may be determined. In solid polyethylene it is shown that not only the deuterons in the crystalline regions but those in the mobile ...
274 citations
TL;DR: In this paper, a temperature-dependent small-angle x-ray scattering and electron microscopic study on a sample of low-density polyethylene affords a determination of the structure changes in a heating and cooling cycle and suggests a new model of partial crystallization and melting.
Abstract: A temperature-dependent small-angle x-ray scattering and electron microscopic study on a sample of low-density polyethylene affords a determination of the structure changes in a heating and cooling cycle and suggests a new model of partial crystallization and melting. The analysis of SAXS data is based upon some general properties of the electron-density correlation function. Electron micrographs are obtained from stained sections γ irradiated at elevated temperatures and are analyzed quantitatively by statistical means. According to the model proposed here the thickness distribution in the amorphous layers, rather than that of the crystalline regions, is the essential factor governing the crystallization and melting behavior. The temperature-dependent changes in this thickness distribution provide a natural explanation for the large reversible changes in long-spacing.
267 citations
TL;DR: A fast and efficient method for analysing ionospheric drift records employing the concepts of full correlation analysis ( Briggs et al., 1950) is described in this paper, where only the most accurately determined experimental data, viz. the width of the mean auto correlogram, and the positions and magnitudes of the maxima in the cross correlograms are required.
124 citations
TL;DR: In this paper, the statistical dynamical theory is reformulated as an extension of the previous theory by taking a more general form of the correlation function of the lattice phase factor.
Abstract: The statistical dynamical theory is reformulated as an extension of the previous theory [Kato (1976). Acta Cryst. A32, 453-457, 458-466] by taking a more general form of the correlation function of the lattice phase factor. A 'static' Debye-Waller factor E and short-range correlation length τ are introduced for characterizing crystalline media. The fundamental equations consist of a set of differential equations for the averaged (coherent) wave fields {(Do),(Dg)} and a set of differential equations for the incoherent part of the intensity fields {Iio, Iig}. They are connected through the transformation to the incoherent beams from the coherent waves. In non-absorbing crystals, energy conservation holds for the total intensities {Ico + Iio, Icg + Iig}, where Ico = |(Do)|2 and Icg = |(Dg)|2. The theory can be applied to the diffraction phenomena of the crystalline materials of any degree of perfection.
111 citations
TL;DR: In this article, data reduction schemes for time differential perturbed angular correlation measurements are evaluated in terms of their relative effectiveness in eliminating irrelevant variables, including single counter efficiencies and spectrum time shifts; and their effectiveness in putting data in a form that can easily be fitted by theoretical correlation functions.
Abstract: Data reduction schemes currently used for time differential perturbed angular correlation measurements are evaluated in terms of (i) their relative effectiveness in eliminating irrelevant variables, including single counter efficiencies and spectrum time shifts; and (ii) their effectiveness in putting data in a form that can easily be fitted by theoretical correlation functions. It is pointed out that erroneous conclusions may be derived from improperly reduced data, but that properly analyzed experiments performed at four angles allow a good determination of both the time-dependent and time-independent parts of the correlation function. Correction of data for accidentals, source self-absorption and spectrum livetime differences are discussed.
107 citations
TL;DR: In this article, the Monte Carlo method was used for high static field operations in Si and GaAs and the variations of diffusion values with the operational frequency or with the 'observation' or sample time were discussed.
Abstract: In Sec. II of this work, we briefly recall the various ways of defining the diffusion coefficient D and discuss their identity in high‐field conditions and in very high frequency operations. In Sec. III, theoretical values obtained by the Monte Carlo method for high static field operations in Si and GaAs are reported and discussed. In Sec. IV, the variations of diffusion values with the operational frequency or with the ’’observation’’ or sample time are studied and tentatively explained.
81 citations
TL;DR: In this article, a perturbation expansion of the local temperature gradient is developed by using a Green's function tensor, and the effective thermal con ductivity can be expressed in series form and the correlation functions of thermal conductivity have been evaluated up to the third order term.
Abstract: This paper presents bounds of effective thermal conductivities for mul ti-component unidirectional short-fiber composites, based upon an ap proach originally developed by the authors for composite effective elastic moduli. A perturbation expansion of the local temperature gradient is developed by using a Green's function tensor. The effective thermal con ductivity can be expressed in series form and the correlation functions of thermal conductivity have been evaluated up to the third order term. It also has been shown that the series expressions obtained by Kroner, and Zeller and Dederichs are approximations of the present solution. The pre sent solution also coincides with Beran's results for statistically isotropic materials, and provides tighter bounds than those of Hashin and Shtrik man, whose approach is equivalent to considering the correlation function up to the second order.
60 citations
TL;DR: In this paper, the Cramer-Rao lower bound and various measures of contrast are considered as possible features in recognition schemes for predicting the magnitude of correlation errors, and the determination of the location of the peak of the correlation function of two similar arrays of picture elements is modeled as a parameter estimation problem.
Abstract: Machines that have been developed to determine the topography of a region from stereo-pair photographs are subject to correlation errors resulting in incorrect elevation calculations. In this paper, the determination of the location of the peak of the correlation function of two similar arrays of picture elements is modeled as a parameter estimation problem. The Cramer-Rao lower bound and various measures of contrast are considered as possible features in recognition schemes for predicting the magnitude of correlation errors. Preliminary simulation results are included.
52 citations
TL;DR: In this article, nonequilibrium molecular dynamics is used to calculate the spectrum of shear viscosity for a Lennard-Jones fluid and it is shown that the amplitude of this long-time tail is between 12 and 150 times larger than what has been predicted theoretically.
Abstract: Nonequilibrium molecular dynamics is used to calculate the spectrum of shear viscosity for a Lennard-Jones fluid. The calculated zero-frequency shear viscosity agrees well with experimental argon results for the two state points considered. The low-frequency behavior of shear viscosity is dominated by anω
1/2 cusp. Analysis of the form of this cusp reveals that the stress-stress time correlation function exhibits at
−3/2 “long-time tail.” It is shown that for the state points studied, the amplitude of this long-time tail is between 12 and 150 times larger than what has been predicted theoretically. If the low-frequency results are truly asymptotic, they imply that the cross and potential contributions to the Kubo-Green integrand for shear viscosity exhibit at
−3/2 long-time tail. This result contradicts the established theory of such processes.
45 citations
TL;DR: In this article, the authors derived expressions for the angular energy flow and the energy-energy angular pattern in perturbative QCD, to order αs, and showed explicitly their infrared safety.
TL;DR: In this article, the mean squared moment of an inner disc, as a function of the diameter of the disc, is fitted with a single dielectric constant, which is thus determined.
Abstract: Molecular dynamics simulation of a sample of a two-dimensional fluid of Stockmayer molecules (i.e. particles interacting via a central Lennard-Jones interaction plus a point dipole interaction) are reported. The dipolar interaction adopted is that required by two-dimensional electrostatics, so that the convergence problem is conserved. The sample (≈13 molecular diameters in size) is kept in vacuo by a steep circular potential barrier. It is first shown that for distances greater than 3 to 5 molecular diameters the macroscopic laws of electrostatics apply, by checking that the mean squared moment of an inner disc, as a function of the diameter of the disc, can be fitted with a single dielectric constant, which is thus determined. The Kirkwood correlation factor for an infinite sample is then evaluated. For highly polar systems, it is greater than unity. Also the radial vector correlation function h Δ(r), which describes the weight of in an expansion of the angle-dependent pair distribution f...
TL;DR: In this article, the steady-state atomic correlation functions of arbitrary order n are given for a system of N superimposed two-level atoms collectively interacting with an imposed C.W. laser field.
Abstract: Exact analytic results for the steady-state atomic correlation functions of arbitrary order n are given for a system of N superimposed two-level atoms (the Dicke model) collectively interacting with an imposed C.W. laser field. Photon statistical studies through the normalised intensity-intensity correlation function, g (2) (0), show that when both N and the driving field become large, g (2) (0) → 1.2. This compares with an earlier approximated calculation 1 ) which allows an independent atomic decay mechanism giving rise to g (2) (0) ≈ 2. Cooperative interactions thus reduce intensity fluctuations. Photon anti-bunching occurs for finite N . There is a second-order phase transition critical bifurcation point in a thermodynamic limit in which N → ∞; a critical exponent is determined.
TL;DR: In this article, the dispersion relation for surface plasmons on a statistically slightly rough surface is obtained from earlier results for the effect of surface roughness on the electrostatic image potential.
Abstract: The dispersion relation for surface plasmons on a statistically slightly rough surface is obtained from our earlier results for the effect of surface roughness on the electrostatic image potential. It is found that this curve consists of two branches, in contrast with the single branch that is obtained in the case of a flat surface. On the basis of a Gaussian model for the correlation function of the surface roughness, explicit results are obtained for the dispersion relation and for a response function that enters the theory of the scattering of electrons by surface plasmons. Our results are similar to those obtained recently by Kretschmann et al. [Phys. Rev. Lett. 42, 1312 (1979)] by a different approach and for a different model of the correlation function of the surface roughness, and are consistent with recent experiments that demonstrate the splitting of the surface-plasmon dispersion relation.
TL;DR: In this article, the authors obtained the two-spin correlation function, in the antiferromagnet for all wavevectors, and in the ferromagnetic network for wavelengths shorter than a coherence length.
Abstract: Rigorous results are presented for the dynamics of the nearest-neighbour Heisenberg chain, for fixed but arbitrary wavevector and frequency, to lowest non-trivial order in the temperature. The authors obtain the two-spin correlation function, in the antiferromagnet for all wavevectors, and in the ferromagnet for wavelengths shorter than a coherence length. The energy correlation function at T=0 is obtained exactly, and is identical in the two systems. They find a violation of dynamical scaling in the form of the spectral function in the antiferromagnet for a range of wavevectors. An extension of the perturbative results for the ferromagnet to treat wavelengths longer than a coherence length shows that the diffusion coefficient vanishes logarithmically, in contrast to the scaling prediction that it is constant. An approximate value for the coefficient of the logarithmic term is obtained which agrees well with the results of simulations.
TL;DR: In this article, a grid-generated turbulent flow has been subjected to a spectrally local perturbation in the form of a high wavenumber, sinusoidal ripple in the mean velocity.
Abstract: A grid-generated ‘isotropic’ turbulent flow has been subjected to a spectrally local perturbation in the form of a high wavenumber, sinusoidal ripple in the mean velocity. It is introduced as the wake of a fine wire, low solidity screen (a ‘zither’), operating below its vortex-shedding Reynolds numbers. The perturbation appears most clearly downstream as a strongly periodic component in the transverse correlation of streamwise turbulent velocity, R11(r2). Its Fourier transform, E11(k2, a ‘one-dimensional spectrum’, shows a corresponding local ‘spike’. The downstream evolution of this perturbation has been chronicled for four different spectral locations. Their decays are approximately exponential. Measurements of the one-dimensional spectrum E11(k1) at several downstream stations show evidence of energy transfer to other wavenumber regions.The decay of the velocity correlation ripple is approximately consistent with the decrease in time of the narrow-band correlation function presented by Comte-Bellot & Corrsin (1971). It is also found that the linear perturbation response calculated by Kraichnan (1959) for a disturbance wavenumber larger than those of the incident turbulence shows fair agreement with this decay.
TL;DR: In this paper, the Coulomb shift Delta f(p12, p1, theta 1) was calculated for HeH+ in its ground state, and the effect of correlation and bond formation on the molecular momentum density rho (p) at RTh approximately 1.4.
Abstract: With the objective of gaining further insight into the effects of correlation on the electronic momentum distribution in small molecules, the authors have calculated the Coulomb shift Delta f(p12) for HeH+ in its ground state. For comparison, the Coulomb hole in position space Delta f(r12) has been reported at the theoretical bond length RTh approximately=1.4. By introducing the distribution function Delta g(p12, p1, theta 1) the authors have been able to examine the effects of correlation with respect to the magnitude and orientation of the momentum p1 for the 'test' electron 1; theta 1 is measured relative to the internuclear axis. Various 'radial' and 'angular' correlation coefficients were determined by evaluating several one- and two-particle expectation quantities, and they also obtained results for the spherically averaged Compton profile. The variations of the radial and angular components of correlation are examined as a function of the internuclear separation R. A brief discussion is also presented concerning the effects of correlation and bond formation on the molecular momentum density rho (p) at RTh approximately=1.4. The authors' results have revealed, once again, that momentum space is especially advantageous for an analysis of electron correlation into its radial and angular contributions.
TL;DR: In this article, the X-ray scattering intensity as a function of angle is calculated by Fourier inversion of γ(r), which can be applied to other systems.
Abstract: A calculation of γ(r), the correlation function which gives the X-ray scattering of a cubic object of uniform density, is given for the full range of r. A new method, which can be applied to other systems, is used. The function γ(r) and its first derivative are everywhere continuous, but γ′′(r) is discontinuous at r = L and r = L□2 (L = cube edge length). This leads to an intersect distribution of unexpected shape. The scattering intensity as a function of angle is calculated by Fourier inversion of γ(r).
TL;DR: In this paper, the results of a previous simulation for a fluid of rigid heteronuclear diatomic molecules using a shifted force, site-site potential, and site site potential were extended to evaluate several time correlation functions for four state points for the orthobaric liquid.
Abstract: The results of a previous simulation for a fluid of rigid heteronuclear diatomic molecules using a shifted force, site-site potential [1] are extended to evaluate several time correlation functions for four state points for the orthobaric liquid. Time autocorrelation functions are reported for the centre of mass velocity, the force, the torque, the angular velocity and the orientational functions P 1 (cos ϑ) and P 2 (cos ϑ). We also report the self and distinct parts of the Van Hove time dependent pair correlation function. The orientational correlation times and functions are compared with experimental results from nuclear magnetic resonance, Raman scattering and far infrared absorption and also with two popular simple models of molecular reorientation; the simulation results are in only moderate agreement with experiment.
TL;DR: In this article, a dynamic Monte Carlo method was used to study the liquid-solid transition of a single freely jointed polymer chain model with van der Waals type intramolecular forces.
Abstract: A dynamic Monte Carlo method has been used to study the liquid–solid transition of a single freely jointed polymer chain model with van der Waals type intramolecular forces. Static and dynamic properties of chains consisting of up to N=63 segments are calculated. The specific heat exhibits a pronounced maximum at the liquid–solid transition temperature which is estimated to kBTc/e=0.3±0.1 (e is the energy parameter). At temperature T
TL;DR: In this article, the rotational and rotovibrational Raman spectra of N2 at 150 K and 585 amagat are compared with the results of a molecular dynamics simulation available in the literature.
Abstract: Orientational correlation functions derived from the rotational and rotovibrational Raman spectra of N2 at 150 K and 585 amagat are compared with the results of a molecular dynamics simulation available in the literature. The angular momentum correlation function is also estimated from the experimental memory function and compared with the one obtained by simulation. Mean square torques, intermolecular correlations and interaction induced contributions are also discussed.
TL;DR: In this article, a simple method to determine the direction and magnitude of flow of a fluorescence-labeled macromolecule in a solution or tissue is proposed, in which the fluorescence correlation function due to fluctuations of fluorescence intensity excited by a rectangular cross-section laser light beam or an ellipsoidal Gaussian laser lightbeam is measured.
Abstract: A new simple method to determine the direction and magnitude of flow of a fluorescence-labeled macromolecule in a solution or tissue is proposed, in which the fluorescence correlation function due to fluctuations of fluorescence intensity excited by a rectangular cross-section laser light beam or an ellipsoidal Gaussian laser light beam is measured. By this method, the contribution of translational Brownian motion of the fluorophore, if any, to the fluorescence correlation function can also be estimated as well as that of flow motion.
TL;DR: In this paper, the spectral turbulent diffusivity (STD) theory was derived from a basic concept of turbulent mixing for the case of homogeneous turbulence, where the contribution to the turbulent flux from eddies of different length is represented by a linear superposition.
Abstract: The spectral turbulent diffusivity (STD) theory, originally deduced from a spectral generalization of the gradient-transfer theory (Berkowicz & Prahm 1979), is here derived from a basic concept of turbulent mixing for the case of homogeneous turbulence. The turbulent mixing is treated in a way similar to Prandtl's mixing-length concept. The contribution to the turbulent flux from eddies of different length is represented by a linear superposition. The spatial variation of the concentration distribution is described in terms of Fourier series. This procedure results in the spectral diffusivity formulation, which is Eulerian and scale dependent. If the concentration distribution is approximated by a truncated Taylor expansion instead of an exact representation by the Fourier series, the gradient-transfer approximation is retrieved.The turbulent energy density, as function of the eddy length, is related to the eddy transport velocity and a probability of the occurrence of the eddies. The eddy transport velocity, derived from the relation between the energy spectrum and the Lagrangian correlation function, is used for computation of the spectral turbulent diffusivity. The turbulent energy spectrum is approximated by the inertial sub-range form as predicted previously.
TL;DR: In this article, it was shown that the noninstantaneous behavior of the velocity correlation function for a turbulent fluid leads to memory effects in the equation of motion of a particle suspended in such a fluid.
Abstract: The noninstantaneous behavior of the velocity correlation function for a turbulent fluid leads to memory effects in the equation of motion of a particle suspended in such a fluid. This effect is a direct consequence of the fluctuation‐dissipation theorem, which connects the correlation properties of the random force with a memory function. As a result, the equation of motion of a suspended particle in a turbulent flow is an integro‐differential rather than a differential equation, and the diffusion coefficient of a suspended particle and that of a fluid do not coincide even in the simplest model. The velocity correlation function of a particle and its diffusion coefficient are found for a simple model.
TL;DR: In this paper, the influence of fluctuations of a relatively weak laser pump on the intensity correlation of resonance fluorescence radiation was studied for a laser acting both below and above the threshold.
Abstract: The influence of fluctuations of a relatively weak laser pump on the intensity correlation of resonance fluorescence radiation is studied for a laser acting both below and above the threshold. Below the threshold the radiation of the laser is characterized by Gaussian properties causing non-factorization of the intensity correlation function. Above the threshold the laser shows non-linear filter properties and, therefore, the deviation of the exact intensity correlation function from its factorized value is small.
TL;DR: In this paper, the authors describe SMJ's analysis more discursively and in terms closer to that used in previous studies of the Ising model, and derive new and more compact expressions for their basic equations.
TL;DR: In this article, the most important structural parameters of a molecular pair-correlation function can be determined approximately by a combination of several scattering experiments, such as neutron (employing different isotopes), X-ray and electron diffraction.
Abstract: Liquid structure is described by the pair-correlation function. If the liquied particles are molecules then the respective correlation function depends on distance and several angular variables; hence, for the sake of simplicity a symmetry-adapted representation must be used. The most important structural parameters of this molecular pair-correlation function can be determined approximately by a combination of several scattering experiments, such as neutron (employing different isotopes), X-ray and electron diffraction. Light scattering, dielectric, and nuclear magnetic relaxation experiments provide further, albeit less direct, access to such determinations. Some results obtained by measurements on chloroform are reported. Theoretical computations of these structural parameters are also discussed.