Showing papers on "Correlation function (statistical mechanics) published in 1974"

Correlation effects in the theory of combined doppler and pressure broadening-i. classical theory*

Abstract: An investigation is conducted of the combined effects of radiator-perturber collisions and radiator translational motion in the context of foreign gas broadening of optical transitions in neutral radiators. Questions concerning the speed-dependent collision frequency are considered and aspects of general theory are explored, taking into account the correlation function, the ensemble average, and the kinetic equation formalism. An elementary solution is discussed along with a one-perturber approximation, inverse power law model calculations, and a comparison with the Voigt profile.

Critical Dynamical Phenomena in Pseudospin-Phonon Coupled Systems

Abstract: The critical dynamical behavior of the pseudospin-phonon coupled system has been investigated in connection with the structural phase transition of molecular crystals. Based on Onsager's equation of motion, explicit expressions for three correlation functions, spin-spin correlation, phonon-phonon correlation and spin-phonon correlation, are obtained. It has been shown that the characteristic of the spectra of these correlation functions shows wide variation depending on the values of two parameters: The ratio of the relaxation rate of reorientational motion of an isolated spin and the frequency of the phonon, and the ratio of the interaction parameter of direct spin-spin coupling and that of spin-phonon coupling. Especially, in `fast relaxation case', the spectrum of phonon-phonon correlation shows critical softening, whereas, in `show relaxation case' the spectrum gives `triple peak' structure and only the central (relaxational) mode shows critical slowing down leaving phonon side peaks unchanged.

Freezing and melting properties of the Lennard‐Jones system

Abstract: Using Monte Carlo simulations, we investigate average molecular arrangements that occur with the fluid‐solid transition in a classical Lennard‐Jones system The crystalline order of the solid phase is explicitly shown by the angularly averaged molecular correlation functions which, in the solid, exhibit a behavior not observed in the fluid The pair and triplet correlation functions delineate the crystalline pattern of the ordered phase out to internuclear separations of many nearest‐neighbor distances A molecular criterion for freezing is reported which claims a proportionality between the values of the pair correlation function in the fluid at the positions of the first and second nearest neighbors The general behavior of the triplet correlation function in the fluid phase is interpreted We also compare predictions for melting pressures and the densities of the coexisting fluid and solid phases

Physical model for strong optical-amplitude fluctuations in a turbulent medium

Abstract: Tatarskii’s geometrical-optics model of scintillation has been generalized to include both diffraction and the loss of spatial coherence of the wave as it propagates through the turbulent medium. An estimate is obtained of the amplitude fluctuations that agrees with the results of perturbation theory for σϒ2⪡1 and saturates to a constant value of the order unity for σT2⪢1 ( σT2 is the amplitude variance calculated on the basis of perturbation theory). In addition, we have calculated the amplitude correlation function. For σT2⪡1, the amplitude correlation function agrees with the results of perturbation theory and for the Kolmogorov spectrum is characterized by a correlation length of the order (L/k)1/2, where L is the propagation distance and k is the optical wave number. Conversely, for σT2⪢1 the amplitude correlation length decreases with increasing propagation distance and is shown to be equal to the lateral coherence length of the wave ρ0(L). In this regime, a residual correlation tail is obtained in agreement with recent experiments.

Structural Relaxation by Digital-Correlation Spectroscopy.

Abstract: : The utility of digital-correlation spectroscopy for investigating structural relaxation in liquids on time scales from 1 miceosec to 1 sec is established. A digital correlator was used to analyze the Rayleigh scattering of light from undercooled glycerol. The correlation function obtained is related to the isothermal structural relaxation dynamics of the liquid. The data were found to join smoothly with those obtained ultrasonically at higher temperatures. (Author)

Properties of Frame-Difference Signals Generated by Moving Images

Abstract: The properties of the frame-difference signals arising from updated "moving" areas and nonupdated "stationary" areas in conditional replenishment interframe encoders are examined. Expressions for the correlation functions and power density spectra of these signals are developed assuming an infinite image field undergoing uniform linear motion. These expressions are modified so as to include the effect of camera integration. Experimentally obtained power spectra are in good agreement with those predicted. Three-dimensional frame-difference correlation functions are evaluated using a realistic image correlation function. The properties of the frame-difference correlation functions in directions parallel and perpendicular to the direction of movement, and in the temporal direction are delineated. It is shown that the correlation function of the frame-difference signal arising from temporally uncorrelated noise is fundamentally different in updated areas compared with nonupdated areas.

Effect of interference between anisotropic scattering entities on light scattering from polymer films. II. The correlation function approach

Abstract: A theory is developed by use of the correlation function approach for calculating both the Hv and Vv intensity of scattered light for a concentrated assembly of spherulities. The scattering becomes a function of the radial and tangential polarizabilities of the spherulite αr and αt, the polarizability αm of the medium, surrounding the spherulites, and the volume fraction ϕs of spherulites. The “effective polarizability of the surroundings” αs, which appeared in previous theories, becomes function of these variables. The theory can explain, for example, why the Vv scattered intensity passes through a maximum during the course of crystallization.

Analysis of intensity correlation spectra of mixtures of polystyrene latex spheres: A comparison of direct least squares fitting with the method of cumulants

Abstract: This paper presents a comparison of direct least squares fitting with the method of cumulants for the analysis of intensity correlation spectra of a mixture of two sizes of polystyrene latex spheres of diameter ratio 1:2. It is demonstrated that both methods lead to mean values of the particle diameters and scattering amplitude ratio which agree with each other within about 5% or less. However, the cumulant analysis depends critically on the choice of the coincidental background for its success. It is observed that for the type of correlation function involved in this study, the formulas necessary to calculate the parameters mentioned above from the cumulants can result in substantial error propagation. Therefore, the cumulants must be known with high precision in order to avoid large uncertainties in the results.

Diffusion of polystyrene in solution studied by photon correlation spectroscopy

Abstract: The diffusion behaviour in toluene, and in some cases toluene + cyclohexane mixtures, of three polystyrenes, two of narrow molecular weight distribution and one of broad molecular weight distribution, has been studied using photon correlation spectroscopy. The apparent diffusion coefficient text-decoration:overlineD increases with increasing concentration in all cases. For a narrow molecular weight sample the correlation function g(1)(K, τ) shows a marked departure from a single exponential decay as the concentration increases, and the possible causes of this behaviour are considered in terms of the theory of the light scattering process. The variation of text-decoration:overlineD with concentration and with molecular weight is examined.

Effects of turbulence in a planetary atmosphere on radio occultation

Abstract: There has been considerable interest in the amplitude and phase fluctuations of the radio signal received from a flyby spacecraft during occultation by a planetary atmosphere. For planetary flyby missions, the Fresnel-zone size exceeds the outer scale size of turbulence, and existing formulations for the frequency spectra of the amplitude and phase fluctuations are inadequate because they do not account for the inhomogeneity of the turbulence in the direction transverse to the propagation path. In this paper, the formulation is given for the correlation functions for the log-amplitude and phase fluctuations of both spherical and plane waves propagating in a turbulent medium whose correlation function for refractive index fluctuations is described by the product of a function of the average coordinate and a function of the difference coordinate. The results are applied to radio occultation of a flyby space probe by the atmosphere of Venus, assuming that the turbulence in the atmosphere exists as a layer, that it is localized, isotropic, and smoothly varying, and that the localized turbulence is described by the Kolmogorov spectrum. Closed-form solutions for both variances and frequency spectra of the log-amplitude and phase fluctuations are obtained using Rytov's method, and it is seen that the shape of the frequency spectra depends a great deal on the characteristics and extent of the turbulence.

Electronic effects in dynamical structure of liquid metals

Abstract: The partial dynamical structure factors of a pure liquid metal are derived from the two-component theory developed in an earlier paper by March and Tosi. In particular, and in contrast to the usual procedure which assumes the hydrodynamic form for the ion-ion dynamical structureSii(q, ω) to be the same as for a classical one-component liquid, in the present theory the contribution to the sound-wave attenuation from single-particle excitations in the conduction electron system is derived explicitly. It is suggested that this is closely related to the anomalous scaling with isotopic mass of the atomic transport coefficients in liquid lithium. The relation to neutron elastic scattering is also established, and some measurements on liquid gallium can be interpreted in a qualitative manner. By studying the charge-charge correlation function for the two-component liquid metal, a theory of electrical resistivity is afforded, which is shown to reduce to Baym’s treatment of the scattering of electrons by the density fluctuations in the limit of weak electron-ion interaction. The relation between the high-frequency conductivity, obtained for arbitrary strength of the electron-ion interaction and the classical Drude-Zener theory is pointed out, and the sum rules for conductivity are seen to be related to those forSii(q, ω) in the limitq→0. A brief discussion of the thermodynamics of the two-component system is included, and related to results for weak electron-ion coupling.

The Direct Estimation of Spatial Wavenumber Spectra of Atmospheric Variables

Abstract: We attempt to determine the zonal kinetic energy and temperature spectra of the large-scale flow in the atmosphere by utilizing observations, unequally spaced, rather than objectively-analyzed grid point values of the wind and temperature variables. Sample correlation functions, are obtained by forming correlations from all possible pair-wise combinations of stations oriented along a parallel of latitude (∼52N). Formally, the estimated line spectrum is given by a Fourier transform of this sample correlation function, Here, owing to the unequal spacing of this sample function, the Fourier transform takes the form of a set of simultaneous, coupled, linear equations, which are poorly conditioned. Four different methods of effecting the solution are tried, all of which are directed at mitigating the ill-conditioning of the system of equations. Spectra of kinetic energy and temperature for the winter and summer seasons are obtained at 850, 500 and 200 mb. There is no significant difference in the shap...

Propagation in statistically irregular waveguides--Part II: Second order statistical moments

Abstract: The correlation function of a point-source field is shown to be governed by the Bethe-Salpeter equation which reduces to the transfer equations for the eigenwave intensities. Because of the boundary irregularities the initial energy distribution among the modes undergoes substantial changes at great distances. In the case of a multimode waveguide the radiation transfer equation takes the form of the diffusion equation in the mode number domain, with the role of time played by the distance along the waveguide. In the framework of the multiple scattering theory developed, the propagation of a time-dependent quasi-monochromatic signal is also discussed. The wall roughness manifests in distortions of the signal shape. In a number of cases explicit expressions have been obtained for the pulse shape as a function of time and coordinates. Typical distances are estimated at which an amplitude modulation is effectively "washed away" by the influence of the multiple scattering.

Quantum corrections to the radial distribution function of a fluid

Abstract: The perturbation theory developed for liquids is used to derive an expression for the first-order quantum correction to the radial distribution function of a fluid. The result is given in terms of grand canonical ensemble distribution functions for the classical fluid. The equations giving the thermodynamic functions in terms of the radial distribution function are discussed, and differences in the quantum and classical cases emphasized. An equation relating the two- and three-body classical distribution functions, derived recently by Singh and Ram using an indirect method, is shown to be simply related to the second equation of the BGY hierarchy.

Tunnel model of liquid diffusion

Abstract: A tunnel model of liquid diffusion, analogous to Barker's thermodynamic model, is constructed by separating particle motion into components parallel and perpendicular to a tunnel axis. By combining exact results for hard rod systems, one is able to predict both the tunnel diffusion coefficient and the corresponding velocity correlation function. The ratio of the tunnel diffusion coefficient to the Enskog value at the same density and temperature is obtained by matching the virial and the temperature. The value predicted lies outside the range investigated by Alder et al; therefore direct comparison to molecular dynamics results is not possible. However, the velocity correlation function has the negative region characteristic of dense fluids. It is suggested that the derivation of the tunnel model dynamics may be valid at close packed densities.

On the dynamics of the classical Heisenberg chain

Abstract: We investigate the space- and time-dependent spin-correlation-function for a linear chain of classical magnetic moments coupled by a purely isotropic exchange interaction. The correlation functions are given in terms of relative variables which at low temperatures turn out to be the normal coordinates appropriate to a system without long-range-order. Analytic expressions for the correlation functions, including correctly the fluctuations responsible for the absence of long-range-order, are given at low temperatures. Well-defined spin wave oscillations exist for wavelengths smaller than the correlation length. In this region our results are consistent with experimental data for the isotropic Heisenberg antiferromagnet TMMC.