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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: In this article, the authors use the matrix formalism to investigate a liquid-crystal system containing impurities and calculate correlation functions for fluctuations of the director orientation and of the order parameter.
Abstract: We use the matrix formalism to investigate a liquid-crystal system containing impurities. As an example, we calculate correlation functions for fluctuations of the director orientation and of the order parameter, which characterizes an isotropic subsystem.
Journal Article
TL;DR: In this paper, a BCS-type variational wave function was used to study attractively interacting quasi-one-dimensional fermionic atomic gases, motivated by cold-atom experiments that access the one-dimensional regime using an anisotropic harmonic trapping potential (with trapping frequencies ωx = ωy ωz) that confines the gas to a cigar-shaped geometry.
Abstract: We use a BCS-type variational wave function to study attractively interacting quasi-one-dimensional fermionic atomic gases, motivated by cold-atom experiments that access the one-dimensional regime using an anisotropic harmonic trapping potential (with trapping frequencies ωx = ωy ωz) that confines the gas to a cigar-shaped geometry. To handle the presence of the trap along the z direction, we construct our variational wave function from the harmonic oscillator Hermite functions, which are the eigenstates of the single-particle problem. Using an analytic determination of the effective interaction among harmonic oscillator states along with a numerical solution of the resulting variational equations, we make specific experimental predictions for how pairing correlations would be revealed in experimental probes, such as the local density and the momentum correlation function.
Journal ArticleDOI
TL;DR: In this article, small angle X-ray scattering using the theoretical apparatus developed by Vonk has been employed to determine the characteristics of the macromolecules of an air-dried fibre of Agave sisalana on the assumption that the material is a tightly packed micellar system.
Abstract: Small angle X-ray scattering using the theoretical apparatus developed by Vonk has been employed to determine the characteristics of the macromolecules of an air-dried fibre of Agave sisalana on the assumption that the material is a tightly packed micellar system. The experimental diffraction curve differs from the Porod law indicating correspondence of the structure of the real system to a non-ideal two phase model characterized by continuous change in the electron density at the phase separation boundary. According to this model the gradient of the mean square of electron density of the isotropic structure is proportional to the fourth moment of the distribution of the intensity of scatter and the second derivative of the correlation function at the origin of coordinates of the back space. The most general approach to analysis of the scattering pattern is offered by the use of the correlation functions which, in principle, contain all the information derived from the experimental curve in the form of the following parameters: mean periodicity in the direction perpendicular to the transitional layer; specific inner surface; volume fraction of the material; volume fraction of the voids; coherent length; dimensions of the corresponding regions in a direction perpendicular to the layer and the parameter of heterogeneity and the volume fraction of the transitional layer.
01 Jan 2008
TL;DR: In this paper, a new model for the thermal conductivity of light liquid alkans has been presented, which may be used in the entire range of liquid phase and is simple and accurate, and may be able to predict the temperature of sample liquids with relative errors smaller than 4%.
Abstract: Thermal conductivity of liquids is an important property in the chemical engineering design, but it is difficult to accurately measure them. Theoretical methods have not also yielded sufficiently accurate and simple expressions for calculating the thermal conductivity of liquids. So, it is customary to use empirical or semi-empirical correlation functions for this purpose. In this work, a new model for the thermal conductivity of light liquid alkans has been presented, which may be used in the entire range of liquid phase. This correlation is simple and accurate, and may be able to predict the thermal conductivity of sample liquids with relative errors smaller than 4%.
Posted Content
TL;DR: In this paper, a nonparametric reconstruction of the statistical properties of penetrable, isotropic randomly rough surfaces from in-plane, co-polarized light scattering data is presented.
Abstract: An approach is introduced for the non-parametric reconstruction of the statistical properties of penetrable, isotropic randomly rough surfaces from in-plane, co-polarized light scattering data. Starting from expressions within the Kirchhoff approximation for the light scattered diffusely by a two-dimensional randomly rough surface, an analytic expression for the normalized surface height correlation function is obtained as an integral over the in-plane and co-polarized scattering data with the introduction of only a couple of additional approximations. The inversion approach consists of two main steps. In the first step the surface roughness is estimated. Next, this value is used to obtain the functional form of the surface height correlation function without initially assuming any particular form for this function (non-parametric inversion). The input data used in validating this inversion approach consist of in-plane and co-polarized scattering data obtained for different forms of the correlation function by either computer simulations or by experiments for two-dimensional randomly rough dielectric or metallic surfaces. Good agreement was obtained between the correlation function and surface roughness obtained during the reconstruction and the corresponding quantities assumed when generating the input scattering data; this was the case for both dielectric and metallic surfaces, for both p- and s-polarized light, and for different polar angles of incidence. The proposed inversion approach provides an accurate, efficient, robust and contact-less method based on in-plane and co-polarized scattering data for the non-parametric characterization of the statistical properties of isotropic two-dimensional randomly rough dielectric and metallic surface.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20224
2021138
2020114
2019138
2018120
2017144