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Correlation function (statistical mechanics)
About: Correlation function (statistical mechanics) is a research topic. Over the lifetime, 6670 publications have been published within this topic receiving 162143 citations.
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TL;DR: For the Q -state Potts model, the authors showed that η = 2 (3v − 1), and for the O( N ) model (−2 ⩽ N⩽ 2), η was shown to be 2 (2v−1) (4v−2).
1,020 citations
TL;DR: In this article, the dielectric correlation function in glasses is calculated and the assumption of short correlation length for normal modes breaks the momentum selection rules and leads to expressions for the first-order Raman-scattering intensity in terms of the density-of-state functions and known frequency-dependent amplitudes.
Abstract: We present a calculation of the dielectric correlation function in glasses showing how the assumption of short correlation length for normal modes breaks the momentum selection rules and leads to expressions for the first-order Raman-scattering intensity in terms of the density-of-states functions and known frequency-dependent amplitudes
971 citations
TL;DR: In this paper, equilibrium correlation functions for a dense classical fluid are obtained by integrating the equation of motion of a system of 864 particles interacting through a Lennard-Jones potential, and the behaviour of the correlation function at large distance and that of its Fourier transform at large wave number are discussed in detail and shown to be related to the existence of a strong repulsion in the potential.
Abstract: : Equilibrium correlation functions for a dense classical fluid are obtained by integrating the equation of motion of a system of 864 particles interacting through a Lennard-Jones potential. The behaviour of the correlation function at large distance, and that of its Fourier transform at large wave number are discussed in detail and shown to be related to the existence of a strong repulsion in the potential. A simple hard sphere model is shown to reproduce very well the Fourier transform of those correlations functions at high density, the only parameter of the model being the diameter a of the hard spheres. (Author)
948 citations
TL;DR: In this paper, the authors present a phenomenological model of intermittency called the P-model and related to the Novikov-Stewart (1964) model, which is dynamical in the sense that they work entirely with inertial-range quantities such as velocity amplitudes, eddy turnover times and energy transfer.
Abstract: We present a phenomenological model of intermittency called the P-model and related to the Novikov-Stewart (1964) model. The key assumption is that in scales N &2-” only a fraction /3n of the total space has an appreciable excitation. The model, the idea of which owes much to Kraichnan (1972, 1974)’ is dynamical in the sense that we work entirely with inertial-range quantities such as velocity amplitudes, eddy turnover times and energy transfer. This gives more physical insight than the traditional approach based on probabilistic models of the dissipation. The P-model leads in an elementary way to the concept of the self-similarity dimension D, a special case of Mandelbrot’s (1974, 1976) ‘fractal dimension’. For threedimensional turbulence, the correction B to the Q exponent of the energy spectrum is equal to +( 3 - D) and is related to the exponent p of the dissipation correlation function by B = Qp (0.17 for the currently accepted value). This is a borderline case of the Mandelbrot inequality B < Qp. It is shown in the appendix that this inequality may be derived from the Navier-Stokes equation under the strong, but plausible, assumption that the inertial-range scaling laws for second- and fourth-order moments have the same viscous cut-off. The predictions of the P-model for the spectrum and for higher-order statistics are in agreement with recent conjectures based on analogies with critical phenomena (Nelkin 1975) but generally diasgree with the 1962 Kolmogorov lognormal model. However, the sixth-order structure function (8v6(Z)) and the dissipation correlation function (e(r) e(r + 1)) are related by
911 citations
TL;DR: Results are very good in both cases, showing that this density-functional model may be used with advantage in the study of the hard-sphere model by itself, or used as a reference system in a perturbative analysis.
Abstract: A free-energy density functional for a system of hard spheres is derived on a semiempirical basis. It is constructed to reproduce the thermodynamics and direct correlation function of a homogeneous fluid and then is tested in two highly inhomogeneous situations: the hard-wall--hard-sphere interface and the hard-sphere solid. The results are very good in both cases, showing that this density-functional model may be used with advantage in the study of the hard-sphere model by itself, or used as a reference system in a perturbative analysis.
898 citations