Failure of the superposition approximation in typical integrals of transport theory

Luckas, Michael; Lucas, Klaus; Breitenfelder-Manske, Hiltrud; Kohler, F.

doi:10.1080/00268978300100371

Cited by 8 publications

(5 citation statements)

References 6 publications

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“…Again, a contribution due to the four-body correlation function has been neglected in equation (4). The parameters a and e relate to the Lennard-Jones (12-6) potential = U~xifl't = (~x~…”

Section: Working Equations For the Viscosity Of Liquid Lennard-jones mentioning

confidence: 99%

“…With x = cos ~ we specify the triplet configuration in addition to two distances. Due to the failure of the superposition approximation for such integrals [4] our procedure in evaluating these integrals J, K and S numerically is to perform Monte Carlo simulations as described in [1] for the pure fluid case and fit the results to a suitable interpolation equation in terms of reduced density and temperature [2].…”

Section: Working Equations For the Viscosity Of Liquid Lennard-jones mentioning

confidence: 99%

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Perturbation theory for the viscosity of molecular liquids and liquid mixtures based on the zero order gaussian memory function approximation

Luckas

Lucas

1985

Molecular Physics

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To cite this article: M. Luckas & K. Lucas (1985) Perturbation theory for the viscosity of molecular liquids and liquid mixtures based on the zero order gaussian memory function approximation, Molecular Physics, 54:1, 225-243,The calculation of the self-diffusion coefficient and the shear viscosity of pure liquids and liquid mixtures using a zero order gaussian memory function is extended to non-spherical molecules by means of a perturbation expansion. The Lennard Jones (12-6) potential was taken for the reference system. Numerical results are presented to illustrate the qualitative effects of the anisotropic shape and the quadrupolar forces on the transport properties. It is shown that the effect of the repulsive site-site forces tends to cancel the influence of the quadrupolar forces. The shear viscosity of the systems Ar-O 2 and N 2 CH 4 is calculated and compared with experimental data. The net influence of anisotropic forces on these mixtures is found to be very small.

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“…Again, a contribution due to the four-body correlation function has been neglected in equation (4). The parameters a and e relate to the Lennard-Jones (12-6) potential = U~xifl't = (~x~…”

Section: Working Equations For the Viscosity Of Liquid Lennard-jones mentioning

confidence: 99%

Section: Working Equations For the Viscosity Of Liquid Lennard-jones mentioning

confidence: 99%

Perturbation theory for the viscosity of molecular liquids and liquid mixtures based on the zero order gaussian memory function approximation

Luckas

Lucas

1985

Molecular Physics

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“…The triplet distribution function can be expanded in spherical harmonics of the triangular shape measured by 0 and 4, 4), (11) lm where the Ytm are spherical harmonics in the convention of Rose [13]. An explicit expression for the expansion coefficients is obtained by multiplying both sides of (11) by the complex conjugate Yzm*, integrating (11) …”

Section: Expansions Of Three-body Functionsmentioning

confidence: 99%

“…A complete characterization of-the approximation embodied in (1) has yet to be made ; however, recent evidence suggests that the superposition approximation is not very satisfactory in many cases [2][3][4][5].…”

Section: Introductionmentioning

confidence: 98%

“…Luckas et al [4] show that certain integrals over g3 may be exactly related, via the hypervirial theorem of statistical mechanics, to finite sums of integrals over the pair function g2. Such relations afford a direct means of testing the superposition approximation and Luckas et al find that for the Lennard-Jones fluid, superposition introduces serious errors into certain integrals over gs.…”

Section: Introductionmentioning

confidence: 99%

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Representation of static three-body correlations in dense fluids

1984

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This paper reports upon new studies of the error involved in the superposition approximation to the triplet distribution function g3 in atomic fluids. The analysis is performed by first expressing g8 in spherical perimetric coordinates (p, 0, ~) in which the 'size' of a triangle, p, is measured independently of its ' shape ' 0 and ~. Then g3 is expanded in spherical harmonics of the triangular shape parameters. The expansion coefficients were evaluated by analysing molecular dynamics simulation data for a Lennard-Jones fluid and the results were compared with the corresponding coefficients appearing in an explicit expansion of the superposition approximation. We show how these two sets of coefficients may be combined to give a precise representation of the difference between the simulation and the superposition correlation functions. This formulation is then tested by evaluating the Axilrod-Teller triple-dipole energy directly from simulation and from the superposition approximation plus correction terms.

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Handling three-body potentials in computer simulation

Rittger

1992

Computer Physics Communications

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Failure of the superposition approximation in typical integrals of transport theory

Cited by 8 publications

References 6 publications

Perturbation theory for the viscosity of molecular liquids and liquid mixtures based on the zero order gaussian memory function approximation

Perturbation theory for the viscosity of molecular liquids and liquid mixtures based on the zero order gaussian memory function approximation

Representation of static three-body correlations in dense fluids

Handling three-body potentials in computer simulation

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