Showing papers on "Correlation function (statistical mechanics) published in 1971"
TL;DR: In this article, the velocity correlation function and the diffusion coefficient are calculated in detail using functional probabilities and compared with those from computer experiments and their significance for real plasma is discussed, and it is shown that in this model diffusion always exhibits the anomalous 1/B variation with magnetic field.
Abstract: Diffusion of plasma in two dimensions is studied in the guiding center model. It is shown that in this model diffusion always exhibits the anomalous 1/B variation with magnetic field. The velocity correlation function and the diffusion coefficient are calculated in detail using functional probabilities. In addition to the 1/B field dependence, the diffusion coefficient is unusual in that it depends weakly on the size of the system. These theoretical results are compared with those from computer experiments and their significance for real plasma is discussed.
239 citations
TL;DR: In this article, the authors compute the correlation functions for the one-dimensional model in the presence of a magnetic field at a constant T = 0, where T is the number of points in the model.
Abstract: We compute the correlation functions $〈{S}_{0}^{x}(t){S}_{R}^{x}(0)〉$ and $〈{S}_{0}^{y}(t){S}_{R}^{y}(0)〉$ at $T=0$ for the one-dimensional $\mathrm{XY}$ model in the presence of a magnetic field.
158 citations
TL;DR: In this paper, the energy of the neutron gas is studied with the Reid and Bressel-Kerman-Rouben soft core potentials up to a density of 4.5 neutrons fm 3, and very approximate estimates for neutron gas and solid energies are presented also for the Hamada-Johnston hard core potential.
146 citations
TL;DR: In this paper, general matrix expressions for solution properties such as chemical potential, partial molal volume and compressibility are developed in terms of (radial) pair distribution functions and of direct correlation functions.
Abstract: General matrix expressions for solution properties such as the chemical potential, partial molal volume and compressibility are developed in terms of (radial) pair distribution functions and of direct correlation functions.
135 citations
TL;DR: In this article, a coupled equation description of the scattering of fast particles is formulated for elastic scattering and two coupled channels are employed, one wavefunction describes the elastic channel and the other is an average wavefunction which takes into account the collisions which remove the incident particles from the elastic channels.
104 citations
TL;DR: In this paper, the optical potential for pions propagating in nuclear matter is investigated from a many-body point of view, and an exact expression for the pion-nucleon correlation function is obtained in terms of the nuclear matter density-density correlation function.
102 citations
TL;DR: In this paper, a theory for the spectra and correlation functions for ion sound turbulence is given, and it is shown that the correlation time can be short enough to affect appreciably the non-linear interactions.
Abstract: A theory is given for the spectra and correlation functions for ion sound turbulence. It is shown that the correlation time can be short enough to affect appreciably the non-linear interactions. The actual value of the anomalous resistivity for plasma in an external electric field is calculated. The ion sound spectra resulting from the non-linear conversion is discussed.
45 citations
TL;DR: In this paper, a Griffiths correlation inequality for Ising ferromagnets is refined and used to obtain improved upper bounds for critical temperatures, and it is shown that, for non-negative external fields, the mean field magnetization is an upper bound for the magnetization of Ising magnetometers.
Abstract: A Griffiths correlation inequality for Ising ferromagnets is refined and is used to obtain improved upper bounds for critical temperatures. It is shown that, for non-negative external fields, the mean field magnetization is an upper bound for the magnetization of Ising ferromagnets.
32 citations
TL;DR: For fluids with molecules in which the electron density can be represented by a rapidly converging expansion in spherical harmonics, the intensity of the X-ray scattering can be obtained from a theory by Steele and Pecora as mentioned in this paper.
31 citations
TL;DR: In this article, the hydrodynamic explanation for the asymptotic t −d 2 decay of time correlation functions for transport coefficients is shown to be equivalent with the mode-mode coupling theory.
29 citations
TL;DR: The theory of small-angle X-ray scattering or light scattering from a system of N randomly distributed, internally homogeneous phases is presented in this paper, where the special case of three components yields a correlation function which is the sum of two exponential terms whose associated correlation lengths are complicated functions of all the interphase surfaces and volume fractions and cannot be interpreted in a simple way.
Abstract: The theory of small-angle X-ray scattering or light scattering from a system of N randomly distributed, internally homogeneous phases is presented. The special case of three components yields a correlation function which is the sum of two exponential terms whose associated `correlation lengths' are complicated functions of all the interphase surfaces and volume fractions and cannot, therefore, be interpreted in a simple way. From the correlation function, three independent parameters are obtained which in principle may be used to determine the three interphase surfaces S21, S23 and S31, provided the volume fractions of the phases are known.
TL;DR: In this paper, a truncated BBGKY hierarchy in the Markovian limit is used to calculate the self and total electron density cross-correlation functions for a partially ionized gas.
Abstract: Kinetic equations for the self and distinct parts of the electron density cross‐correlation function are obtained for a partially ionized gas by solving a truncated BBGKY hierarchy in the Markovian limit. Assuming a BGK model for the terms representing collisions with the neutrals, these equations are then used to calculate the self and total electron density cross‐correlation functions. The expressions obtained for the correlation functions are valid for stationary, homogeneous, partially ionized plasmas. In equilibrium, the expression for the spectral density reduces to that obtained by Dougherty and Farley. In the limit of zero‐collision frequencies, the results of Rostoker and Rosenbluth are recovered. For long times and large probe separations analytical expressions are obtained for the cross correlation functions. It is found that the self‐correlation function depends on the electron diffusion coefficient and the total electron correlation function depends on the ambipolar diffusion coefficient.
TL;DR: The angular velocity correlation function can be studied through measurements of dielectric relaxation and far-infrared absorption, and the data of Davies, Pardoe, Chamberlain, and Gebbie are analyzed in this article.
Abstract: The angular velocity correlation function can be studied through measurements of dielectric relaxation and far‐infrared absorption. Relations between these quantities are described in this article, and the data of Davies, Pardoe, Chamberlain, and Gebbie are analyzed. Velocity correlation times are obtained for molecules in four simple liquids. Hubbard has obtained a theoretical expression linking the velocity correlation time, the orientation correlation time, and the molecular moment of inertia. This expression is experimentally verified for molecules in nonviscous liquids. Certain paradoxical predictions are found when this expression is applied to viscous liquids and solids. This article considers stochastic models for relaxation, in which the probability of molecular reorientation is modulated by fluctuations in the intermolecular environment. These stochastic models lead to orientation and velocity correlation functions that are consistent with experimental observations.
TL;DR: A solution for the time evolution of the velocity correlation function in homogeneous isotropic turbulence is obtained using multipoint distribution functions in this paper, where the dependence of the correlation function on the fluid parameters is calculated for a simple initial condition.
Abstract: A solution for the time evolution of the velocity correlation function in homogeneous isotropic turbulence is obtained using multipoint distribution functions. The dependence of the velocity correlation function on the fluid parameters is calculated for a simple initial condition.
TL;DR: In this paper, the contribution of disorder scattering by imperfect spherulites resulting from fluctuations in the magnitude of the anisotropy is analyzed for two-dimensional spheroidites.
Abstract: The contribution to the disorder scattering by imperfect spherulites resulting from fluctuations in the magnitude of the anisotropy is analyzed for two-dimensional spherulites. The fluctuations are described in terms of a parameter characterizing the meansquare amplitude of the fluctuation and a correlation function describing the distance over which the correlation occurs. Cases considered are those where the correlation depends on either the radial or the angular separation of the scattering volume elements. As with the case of disorder in orientation, one finds that disorder in anisotropy may result in a nonzero value of intensity at μ = 0° and 90°, a decrease in the higher-order variation of scattered intensity with θ, and an increase in the intensity of scattering at higher values of θ over that for a perfect spherulite. In addition, disorder in the angular direction leads to an increase in the scattered intensity at small values of θ as compared with the zero intensity of scattering from a perfect spherulite at θ = 0°.
TL;DR: In this article, the Fourier components of the density-density correlation function in a fluid obtained from the linearized hydrodynamic equations can also be obtained by adopting a particularly simple form for the associated memory function.
Abstract: It is shown that the expression for the Fourier components of the density-density correlation function in a fluid obtained from the linearized hydrodynamic equations can also be obtained by adopting a particularly simple form for the associated memory function The result is used to calculate the longitudinal viscosity of a fluid in terms of the moments of the space and time Fourier transform of the density-density correlation function S(q, ω)
TL;DR: In this paper, a closed expression similar to the Ursell-Mayer expansion is obtained for the static multiple density correlation function In = ǫk1⋯ρkn, which breaks into products of lower ones, if there exist partial momentum conservations among the k's.
Abstract: A closed expression similar to the Ursell‐Mayer expansion is obtained for the static multiple density correlation function In=〈ρk1⋯ρkn〉 of a many‐particle system. It is shown that In breaks into products of lower ones, if there exist partial momentum conservations among the k's. Using the convolution approximation for the n‐particle correlation function, we evaluate In in a closed form. The result is shown to be accurate in the small k region.
TL;DR: In this article, a computer correlation technique is described for comparing observed magnetic anomaly profiles to model profiles generated from a paleomagnetic time scale, where a model is computed for a given spreading rate, divided into small segments, and each segment is then compared to a corresponding unit of the data profile.
Abstract: A computer correlation technique is described for comparing observed magnetic anomaly profiles to model profiles generated from a paleomagnetic time scale. A model is computed for a given spreading rate, divided into small segments, and each segment then compared to a corresponding unit of the data profile. Each model segment is systematically shifted and correlated with the data, and the resulting correlation functions are displayed in an ‘offset-age’ diagram. Interpretation of this diagram reveals possible histories involving faulting or changes of spreading rate that may be overlooked by the visual method, and quantitative estimates of the uncertainties in the spreading rates may be made.
TL;DR: In this article, an experimental determination of the pair and direct correlation functions of polystyrene latex spheres in the high density limit has been made and from these the pair potential for hard spheres has been calculated.
Abstract: An experimental determination of the pair and direct correlation functions of polystyrene latex spheres in the high‐density limit has been made. From these the pair potential for hard spheres has been calculated. The significance of the functions as they bear on the Percus—Vevick and the hypernetted chain approximation is discussed.
TL;DR: In this article, it was shown that the diagrams that correspond to the first renormalization equation for the coherent field, in a statistically homogeneous and isotropic medium, are the dominant diagrams.
Abstract: In this work it is shown that the diagrams that correspond to the first renormalization equation for the coherent field, in a statistically homogeneous and isotropic medium, are the dominant diagrams. To study the cumulative effect of the omitted diagrams, which increase in number with each power of the expansion parameter ∈, we sum the next largest omitted diagrams. This sum is proportional to the propagation path length times the usual first renormalization solution. The above analysis and a more compact one that utilizes the full Dyson equation both yield a validity criterion that is basically distance independent. The derivation of the validity criterion is primarily based on two observations that are not used by other authors. First we note and account for the fact that the solution of the first renormalition integral equation is always approximated. Secondly, we utilize the simple observation that phase accumulation and rate of decay are unimportant if the amplitude of the wave is already insignificant. We obtain the same criterion as other authors for kol ≫ 1, where ko is the free space wave number and l is the correlation length of the dielectric fluctuations; for kol ≪ 1 the criterion is new. Finally, a relatively simple method of solving the first renormalization integral equation for the correlation function of the field is presented for the case kol ≫ 1 and some justification for the validity of this equation is given.
TL;DR: The results of a theory-experiment comparison of the absolute electromagnetic wave backscatter from a neutral gas dominated turbulent argon arc plasma jet are reported in this paper, for various aspect angles and covers a range of rms electron density fluctuations extending beyond critical.
Abstract: The results of a theory‐experiment comparison of the absolute electromagnetic wave backscatter from a neutral gas dominated turbulent argon arc plasma jet are reported. The study is carried out at 16 GHz, for various aspect angles and covers a range of rms electron density fluctuations extending beyond critical. The backscatter power is measured using a homodyne detection system. The calculation, based on the unmodified Born scattering model, consists of a volume weighting of the turbulent plasma properties, 〈δne2 and S(k), by the antenna illumination. The determination of S(k), the three‐dimensional spectral density function, makes use of the measured space‐time correlation function and frequency spectrum of electron density fluctuations, Taylor hypothesis, and a three‐dimensional MacDonald function analysis. The Born theory is found to describe the backscatter within about 3 dB right up to critical. This result is thought to be due in part to attenuation of the coherent antenna field by large density fl...
TL;DR: The density derivative of the timedependent pair correlation function is related to the time-dependent triplet correlation function as discussed by the authors, which is a generalization of the density hierarchy for the equilibrium correlation functions.
TL;DR: In this article, a revised version of the scaling theory of equilibrium critical phenomena is proposed, which is based on hypotheses which differ only slightly from those set forth in original scaling theory.
Abstract: Here proposed is a revised version of the scaling theory of equilibrium critical phenomena. This revised theory is based on hypotheses which differ only slightly from those set forth in original formulations. The conclusions reached are essentially equivalent to those of Stell's weak scaling theory. One obtains relations which require prior knowledge of three exponents for the derivation of the rest. An additional exponent, denoted w, enters certain relations containing exponents which pertain to the correlation function. This exponent must be greater than or equal to one in order to satisfy certain generally accepted inequalities. An argument for why w should be greater than or equal to one is formulable within the framework of the original hypotheses of scaling theory. While the revised theory has the drawback of containing an extra unknown, it is nevertheless capable of reconciling scaling theory with other theories of critical exponents.
TL;DR: In this paper, the decisive role of non-linear terms in the equation for the spin correlation function for temperatures close to the Curie point has been demonstrated, and it has been shown that nonlinear terms are crucial for spin correlation.
TL;DR: In this article, the spatial and temporal correlation function of the sea surface, quantities required in underwater acoustic studies, can be formulated via the surface wave energy spectrum, and two spectral functions, proposed by Neumann-Pierson and by Pierson-Moskowitz for a fully developed sea, time and space correlation functions are calculated numerically.
Abstract: The spatial and temporal correlation function of the sea surface, quantities required in underwater acoustic studies, can be formulated via the surface‐wave energy spectrum. For two spectral functions, proposed by Neumann‐Pierson and by Pierson‐Moskowitz for a fully developed sea, time and space correlation functions are calculated numerically. The latter ones, although functions of two variables, can be constructed from two auxiliary functions, dependent only on correlation distance, when a cosine‐squared law for the directionality of the wave spectrum is assumed. These auxiliary functions are tabulated and plotted. The two spectra produce results that differ only slightly.
TL;DR: In this paper, the correlation functions of the number density in μ space are derived, for a neutral gas and a plasma in equilibrium, from the two-time Liouville equation, after sufficient smoothing has taken place.
Abstract: Equations for the correlation functions of the number density in μ space are derived, for a neutral gas and a plasma in equilibrium, from the two time Liouville equation. For the neutral gas, after sufficient smoothing has taken place the equation becomes the linearized Boltzmann equation. For the plasma the “collision” term is approximated and the equation solved for the correlation functions in space. The electron‐electron function is examined in the limit of zero wavenumber and lowest order in the mass ratios and shows that, due to electron‐ion collisions, the resonance is shifted from the collisionless result ωe and has a width proportional to ωe times the plasma parameter.