Showing papers on "Correlation function (statistical mechanics) published in 1979"

Photon correlation spectroscopy of particle distributions

Abstract: A least‐squares method for correlation function profile analysis using a histogram approximation is described. The method is completely general, especially for bimodal distributions, and compares favorably with the method of cumulants. The measured photoelectron time‐correlation function yields a histogram of the linewidth distribution which can be related uniquely to the particle size. The analysis is tested using simulated data with unimodal and bimodal size distributions. In our verification of the method using aqueous suspensions of Dow latex spheres, we have shown that our method is not only consistent with the results from electron microscopy, but that it is more precise and truly measures the hydrodynamic size of particles suspended in fluids.

Asymptotic properties of Burgers turbulence

Abstract: The asymptotic properties of Burgers turbulence at extremely large Reynolds numbers and times are investigated by analysing the exact solution of the Burgers equation, which takes the form of a series of triangular shocks in this situation. The initial probability distribution for the velocity u is assumed to decrease exponentially as u → ∞. The probability distribution functions for the strength and the advance velocity of shocks and the distance between two shocks are obtained and the velocity correlation and the energy spectrum function are derived from these distribution functions. It is proved that the asymptotic properties of turbulence change qualitatively according as the value of the integral scale of the velocity correlation function J, which is invariant in time, is zero, finite or infinite. The turbulent energy per unit length is shown to decay in time t as t−1 (with possible logarithmic corrections) or according as J = 0 or J ≠ 0.

Statistical theory of the elastic constants of nematic liquid crystals

Abstract: A statistical mechanical theory of the Frank elastic constants is formulated. The free energy functional is constructed for the deformed sample and the free energy density is defined for the case of small spatial gradients. The Frank constants are expressed in terms of the direct correlation function c(1, 2) and the orientational single particle distribution function. For the example of Onsager spherocylinders three constants K 1, K 2 and K 3 are calculated. The results of these calculations are similar to those given by Priest and by Straley.

Molecular dynamics of liquids modelled by '2-Lennard-Jones centres' pair potentials

Abstract: The molecular dynamics study based on two-Lennard-Jones (12-6) centres pair potentials, with reduced bond lengths in the range 0·5 ⩽l/σ⩽0[sbreve]d8, and with e, σ-parameters simulating liquid F2, Cl2, Br2 and CO2 (14) is extended to time correlation functions. The calculated properties include: translational velocity and force self correlation functions; orientational self-correlation functions , a cross correlation function for P 2, angular momentum (J), and torque self-correlation functions. Diffusion constants (D) and rotational relaxation times (τ1, τ2, τ J ) have been evaluated and where possible compared with experimental data (D and τ J for F2, τ2 for Cl2). Calculations with 108 or 256 molecules are reported for several densities and temperatures for four model liquids. The nature of the one-particle motion is analysed qualitatively in terms of quasi-oscillations and -librations. It is difficult to fit the observed features into the framework of physical models proposed in the lite...

The orientational correlation parameter for liquid CS2, C6H6 and C6F6

Abstract: The values of the second rank orientational correlation function g 2 and the effective polarizability anisotropy of liquids CS2, C6H6 and C6F6 were determined by combining data from the Rayleigh spectrum with Cotton-Mouton measurements on these liquids in a way which avoids difficulties with the interaction-induced polarizability A detailed discussion of the errors associated with this procedure is presented The values are used to interpret the Kerr constants of these liquids The value of g 2 is combined with Rayleigh and Raman reorientational relaxation times to determine the dynamic orientational correlation parameter Comparison with previous values suggests the plausibility of calculating the effective polarizability in a dielectric model

X-ray and Neutron Diffraction from Liquid Alkali Metals

Abstract: This paper deals with the accurate determination of the structure factors of three liquid alkali metals: Na, K and Cs. Special attention has been paid to the experimental aspects: the design of the X-ray and neutron goniometers including the sample holders and the corrections to be applied to the rough experimental results. An assessment of the accuracy achieved has been made, mainly by comparison with existing physical data. In order to interpret the final results, theoretical calculations with hard-sphere models have been carried out and a comparison with the results of computer experiments, based on more realistic potentials, has been made. Some physical quantities related to the structure factor (pair distribution function, direct correlation function, pair potential and electrical resistivity) have been calculated.

Scaling, equation of state, and the instability of the spin-glass phase

Abstract: The free energy and equation of state for the Ising-type random-bond spin-glass are generated in $6\ensuremath{-}\ensuremath{\epsilon}$ dimensions with the aid of renormalization-group recursion relations. Scaling predictions based on previous renormalization-group work are borne out. The specific heat is found to be smooth with a rounded peak above the transition temperature, and the order-parameter exponent $\ensuremath{\beta}$ is greater than 1. We also find, however, that the spin-glass phase is unstable in that certain fluctuations have a negative gap. This instability leads immediately to the nonphysical prediction that the bond average of the square of a spin correlation function is negative. We conclude that there is a serious flaw in current approaches to the spin-glass phase based on the Edwards-Anderson order parameter.

The shape of collision broadened lines from resonance to the far wings

Abstract: A line shape for collision-broadened lines applicable from the resonance region to the far wings is developed. An empirical correlation function is used to represent the known short and long time behavior of the true correlation function and to interpolate the unknown intermediate time regime. The resulting spectral shape is a simple analytic function which reduces to essentially the Van Vleck-Weisskopf equation when |ω−ω0|τ2⪡1, but which smoothly assumes an exponential behavior in the far wings where |ω−ω0|τ2⪢1. The time parameter, τ2, is a measure of the duration of collision and is related to the mean squared torque produced in bimolecular collisions. The effect of overlapping lines, also variations in the model correlation function on the line shape are considered. The theory is applied to the absorption in the high-frequency far wing of the 4.3υ band in CO2.

A small angle X-ray scattering study of polyethylene fibres, using the two-dimensional correlation function

Abstract: By Fourier transformation of the intensity distribution in the small angle X-ray scattering diagram of a polymer fibre one obtains the corresponding two-dimensional correlation function. This is compared with correlation functions calculated on the basis of different models of the semi-crystalline morphology. Here, two steps may be distinguished: in the first, the correctness of a model may be checked with the aid of qualitative features, such as the relative positions and sizes of positive and negative areas; in the second a quatitative agreement is pursued by fixing the various parameters involved. This method was applied to cold drawn low density polyethylene before and after annealing at different temperatures. In the case of the non-annealed sample, the microparacrystalline model, discussed byHosemann andLoboda-Cackovic (J. Appl. Cryst.11, 540 (1978)) was found to give the best fit. Annealing at 80 °C or higher temperatures seems to lead to what has been indicated as a three-dimensional chess-board structure; it consists of fibrils in which crystalline and amorphous regions alternate in such a way that the crystalline regions in a fibril are adjacent to amorphous regions in neighbouring fibrils.

Self-diffusion beyond Fick's law

Abstract: The Van Hove self-correlation function, the intermediate incoherent scattering function and its Laplace transform are determined asymptotically for a one component fluid in equilibrium, using the mode coupling theory. The results reproduce in the hydrodynamic limit the predictions from Fick's law. The corrections to Fick's law are consistent with a long time tail in the velocity correlation function and with a diverging super Burnett coefficient in the linear diffusion equation.

Electrical Resistivity of Liquid Metals in Regime of Short Mean Free Path

Abstract: Using the force-force correlation function formula for electrical resistivity, plus an approximate result of Bardeen for the effect of scattering on the off-diagonal elements of the density matrix, a self-consistent method of calculating the electronic mean free path in liquid metals is proposed.

Incoherent scattering near a sol gel transition

Abstract: We consider the self correlation function for one monomer in a gelating system near the sol gel transition. Our analysis is based on the Stauffer distribution function for cluster sizes, plus a scaling ansatz for the viscosity at different spatial scales. 1) In the sol phase, the intermediate scattering function Ik(t) (for wavevector k) is predicted to decrease like t-β/( ν+s) where β, v, and s are critical exponents for the gel fraction, the correlation length, and the macroscopic viscosity (t being the time). 2) In the gel phase, Ik (t → ∞) is finite and defines a Debye Waller factor. Near k = 0, this is equal to the gel fraction. These properties might be checked by photon beat methods, using a dilute set of labelled monomers.

Phonon characterisation and the theory of the temperature dependence of the electrical resistivity of amorphous metals

Abstract: The dependence of the dynamic and static structure factor and the temperature-dependent part of the electrical resistivity on the spatial correlations of the lattice vibrations is investigated. For this purpose an amplitude correlation function for the lattice vibrations is introduced and expressed in terms of a correlation length. The authors' numerical model calculations show that a negative temperature coefficient of the electrical resistivity is favoured by a short correlation length.

An accurate equation of state of a hard convex body fluid mixture

Abstract: A method enabling to calculate the contact-point values of the pair correlation function of convex body fluids from a semi-empirical equation of state is presented and the accurate Nezbeda equation of the pure hard convex body fluid is extended to mixtures. Comparison of results for one- and two-component systems with Monte Carlo simulation data shows excellent agreement.

Spinodal decomposition in a Lennard-Jones fluid

Abstract: A microscopic theory for the early stages of spinodal decomposition in a one-component fluid is presented. We show that in the unstable region of the phase diagram the amplitude of density fluctuations with wave vectors less than some critical value qc , where qc is the position of the pole in the static density response function of the uniform fluid, increases exponentially with time. The corresponding amplification factor is related to the Ornstein-Zernike direct correlation function of the uniform fluid. We have calculated the amplification factor for a Lennard-Jones fluid at several densities and temperatures. We find that these amplification factors are qualitatively different from those obtained from the analogue of Cahn's linearized theory of spinodal decomposition. Our calculated value of qc at reduced density 0·35 and temperature 0·8 is in fairly good agreement with the result of a recent molecular dynamics simulation of a Lennard-Jones fluid quenched to this state.

A semi-analytic theory for the static properties of a one component plasma

Abstract: A universal functional form is proposed for the direct correlation function of the one-component plasma This form depends on only one scaling parameter which is determined from a novel hypernetted-chain compressibility equation through a single numerical integration The results compare well with the numerical solutions of the hypernetted-chain integral equation as well as with recent Monte Carlo computations

A study of the rotational correlation function for cyclohexane by Raman scattering

Abstract: The rotational correlation function of cyclohexane has been obtained by Raman spectroscopy in the liquid and plastic crystal phase. The characteristic relaxation time for reorientation of the molecular symmetry axis rises from 0·6 ps at 345 K to 2·5 ps at 195 K. Comparison with the J and M extended diffusion model indicates closer agreement with the latter.

A statistical model for groupiness in wind waves

Abstract: A simple nonspectral model for wind waves is proposed It is found that a model based on a single ‘carrier’ wave with random phase shifts between groups reproduces the essential characteristics of the autocorrelation function of real wind waves It is not purported to be a general wind-wave model but is used simply to explain the statistical significance of the tail of the correlation function and to obtain good masking functions for the computation of smoothed wave spectra Engineering applications of such simple wave models are briefly discussed

Correlation of geologic logs with spectral methods

Abstract: Spectral studies of geologic logs demonstrate that automatic well—log correlation can be processed more efficiently in the frequency domain. Cross correlation of the power spectra of well logs identifies the direction and degree of thickening of stratigraphic sequences between two wells. Given the stretch, the displacement between logs is computed by correlation processes without relying on iterative procedures. Beginning with digitized log data of unequal lengths, power spectra are computed. The stretch factor between the two logs is observed as a difference in frequency scaling. A transform to logarithmic frequencies converts the spectra to a form that reduces the scaling effect of the frequencies to a simple displacement between the plots. A Lagrange interpolation procedure permits cross correlation of the two spectra with a variable window size. The peak value of the resultant correlation function identifies the displacement between the spectra and this, in turn, permits calculation of the stretch factor.

A memory function model for the velocity autocorrelation function and the self-diffusion coefficient in simple dense fluids

Abstract: A memory-function model is used to compute the velocity autocorrelation function and the self-diffusion coefficient of a dense Lennard-Jones fluid from the zero-time correlation functions of the molecular velocity and its first two time derivatives. It is shown that these zero-time correlation functions can be evaluated in terms of the radial distribution function and the pair potential only, i.e. without considering higher order correlation functions. Since molecular dynamics results are available for the radial distribution function as well as the velocity autocorrelation function and the self-diffusion coefficient, a rigorous test of the chosen memory function is possible. The agreement is reasonable, although generally not within the error bands of the molecular dynamics results.

Experimental Investigation of Some Statistical Properties of Monochromatic Speckle Patterns

Abstract: Statistical properties of monochromatic, polarized speckle patterns were studied experimentally. The intensity correlation function, the probability density of the spatial derivative of the intensity, and the average number of level crossings of the intensity were measured. The results are compared with theory and a high measuring accuracy obtained using lock-in detection.

Spin Wave Theory of the Spin 1/2 XY Model

Abstract: The spin wave theory of Kondo and Yamaji is applied to the spin 1/2 XY model in one to three dimensions. In one dimension, the value of the gap Δ which appears in the spectrum of x -component spin remains finite up to 0 K, and no phase transition occurs. The value of the nearest neighbour correlation function is in good agreement with the exact values. In three dimensions, Δ vanishes at a finite temperature, and the second order phase transition occurs. In two dimensions, as T →0, Δ becomes very small for square lattice and tends to zero as exp (- T 0 / T ) for triangular lattice, which means the non-existence of the phase transition. The susceptibility, however, becomes anomalously large for low temperatures, and the extrapolation of Curie-Weiss law gives a “fictitious” transition temperature whose value agrees with those given by the high temperature expansion and the real space renormalization group theory.

Solution of the Ornstein-Zernike equation for a soft-core Yukawa fluid

Abstract: A model for simple fluids is proposed in which the radial distribution function has a parametric form appropriate to a soft-core fluid for interparticle separationr ⩽ R, whereR is some range parameter. Forr > R, the direct correlation function is assumed to be of Yukawa form. The Ornstein-Zernike equation is solved for this system, yielding the radial distribution and the total correlation function for the entire range of interparticle separation. Methods of relating the model fluid to a real fluid by assigning values to the parameters are discussed.