DOI: 10.1063/1.463652. Liquid-state integral equations at high density: On the mathematical origin of infinite-range oscillatory solutions

Liquid-state integral equations at high density: On the mathematical origin of infinite-range oscillatory solutions

10.1063/1.463652

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Analytic asymptotic analysis and finite element numerical procedures are used to elucidate the mathematical reasons for the appearance of infinite-range oscillatory solutions to certain integral equation theories of wall–fluid interfacial structure and liquid state radial distribution functions. The results contribute to two issues of recent debate: (i) what physical significance (if any) can be attributed to the apparent ‘‘solidlike’’ structure that is often (but not always) seen in high density solutions to liquid state integral equation theories and (ii) is the same mathematical structure present in density functional theories (i.e., in the presence of a variational condition arising from a free energy functional)?

Bibliography

Henderson, J. R., & Sabeur, Z. A. (1992). Liquid-state integral equations at high density: On the mathematical origin of infinite-range oscillatory solutions. The Journal of Chemical Physics, 97(9), 6750â6758.

Authors 2

J. R. Henderson (first)
Z. A. Sabeur (additional)

References 27 Referenced 42

10.1063/1.1750949 / J. Chem. Phys. (1941)
10.1103/PhysRevB.19.2775 / Phys. Rev. B (1979)
10.1063/1.441326 / J. Chem. Phys. (1981)
10.1063/1.454287 / J. Chem. Phys. (1988)
10.1063/1.460219 / J. Chem. Phys. (1991)
10.1063/1.461266 / J. Chem. Phys. (1991)
10.1080/00268979100100711 / Mol. Phys. (1991)
{'key': '2024020710200239200_r6a'}
10.1103/PhysRevA.31.2672 / Phys. Rev. A (1985)
10.1103/PhysRevA.32.2909 / Phys. Rev. A (1985)
10.1103/PhysRevA.40.2567 / Phys. Rev. A (1989)
10.1080/00018737900101365 / Adv. Phys. (1979)
10.1103/PhysRevA.45.3823 / Phys. Rev. A (1992)
{'key': '2024020710200239200_r11a'}
10.1080/00268978700102611 / Mol. Phys. (1987)
{'key': '2024020710200239200_r12a'}
10.1080/00268978500102521 / Mol. Phys. (1985)
10.1063/1.434014 / J. Chem. Phys. (1977)
10.1063/1.439436 / J. Chem. Phys. (1980)
10.1063/1.443033 / J. Chem. Phys. (1982)
10.1063/1.1671624 / J. Chem. Phys. (1969)
10.1080/00268978700100381 / Mol. Phys. (1987)
10.1080/00268978400100651 / Mol. Phys. (1984)
{'key': '2024020710200239200_r18a', 'first-page': '409', 'volume': '410', 'year': '1987', 'journal-title': 'Proc. R. Soc. A'} / Proc. R. Soc. A (1987)
{'key': '2024020710200239200_r19'}
{'key': '2024020710200239200_r20'}
10.1063/1.456420 / J. Chem. Phys. (1989)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 8:20 a.m.)
Deposited	1 year, 6 months ago (Feb. 7, 2024, 11:09 a.m.)
Indexed	5 months, 1 week ago (March 22, 2025, 4:30 a.m.)
Issued	32 years, 9 months ago (Nov. 1, 1992)
Published	32 years, 9 months ago (Nov. 1, 1992)
Published Print	32 years, 9 months ago (Nov. 1, 1992)

Funders 0

None

BibTeX

@article{Henderson_1992, title={Liquid-state integral equations at high density: On the mathematical origin of infinite-range oscillatory solutions}, volume={97}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.463652}, DOI={10.1063/1.463652}, number={9}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Henderson, J. R. and Sabeur, Z. A.}, year={1992}, month=nov, pages={6750–6758} }

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