Evaluation of numerous J-, K-, L-, M-, and N-integrals used in perturbation theory: Integral raw data

Cite as:

Gottschalk, Matthias (2021): Evaluation of numerous J-, K-, L-, M-, and N-integrals used in perturbation theory: Integral raw data. GFZ Data Services. https://doi.org/10.5880/GFZ.3.6.2021.002

Status

I N R E V I E W : Gottschalk, Matthias (2021): Evaluation of numerous J-, K-, L-, M-, and N-integrals used in perturbation theory: Integral raw data. GFZ Data Services. https://doi.org/10.5880/GFZ.3.6.2021.002

Abstract

Following Barker, Pople and Gubbins & Gray, the u-expansion of the perturbation theory, used for developing equations of state for fluids, requires sets of J-, K-, L-, M-, and N-integrals as a function of rho* and T*. These integrals are calculated here from pair and triplet correlation functions, which were derived in a previous communication, using particle configurations from extensive Monte-Carlo simulations of a Lennard-Jones fluid.

The pair and triplet correlation functions are based on 27615 state points covering a rho*-T* space from 0.002-1.41 and 0.45-25 in reduced variables, respectively, which is also the range of the calculated integrals. Quadruplet correlation functions, required by the M- and N-integrals, were calculated using the trans-superposition approximation, using pair and triplet correlation functions. Here the unfitted raw data of 597 J-, 90 K-, 256 L-, 4M-, and 4N-integrals are reported. The number of available values at different rho*-T* state points are 27615 for the J-integrals, and in the range of 6999-7053, 6789-7055, 6440-6587, 6544-6751 for the K-, L-, M-, andN-integrals, respectively.

Authors

Gottschalk, Matthias;GFZ German Research Centre for Geosciences, Potsdam, Germany

Contact

Gottschalk, Matthias; GFZ German Research Centre for Geosciences, Potsdam, Germany;

Keywords

Monte-Carlo simulations, Lennard-Jones fluid, configurations, pair-correlation functions, triplet-correlation functions, pair-integrals, triplet-integrals

GCMD Science Keywords

EARTH SCIENCE SERVICES > MODELS > PHYSICAL/LABORATORY MODELS

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