A numerical bifurcation analysis of the ornstein-zernike equation with hypernetted chain closure
(2007) In SIAM Journal on Scientific Computing 29(6). p.2442-2463- Abstract
We study the codimension-one and -two bifurcations of the Ornstein-Zernike equation with hypernetted chain (HNC) closure with Lennard-Jones intermolecular interaction potential. The main purpose of the paper is to present the results of a numerical study undertaken using a suite of algorithms implemented in MATLAB and based on pseudo arc-length continuation for the codimension-one case and a Newton-GMRES method for the codimension-two case. Through careful consideration of the results of our computations, an argument is formulated which shows that spinodal isothermal solution branches arising in this model cannot be reproduced numerically. Furthermore, we show that the existence of an upper bound on the density that can be realized on a... (More)
We study the codimension-one and -two bifurcations of the Ornstein-Zernike equation with hypernetted chain (HNC) closure with Lennard-Jones intermolecular interaction potential. The main purpose of the paper is to present the results of a numerical study undertaken using a suite of algorithms implemented in MATLAB and based on pseudo arc-length continuation for the codimension-one case and a Newton-GMRES method for the codimension-two case. Through careful consideration of the results of our computations, an argument is formulated which shows that spinodal isothermal solution branches arising in this model cannot be reproduced numerically. Furthermore, we show that the existence of an upper bound on the density that can be realized on a vapor isothermal solution branch, which must be present at a spinodal, causes the existence of at least one fold bifurcation along that vapor branch when density is used as the bifurcation parameter. This provides an explanation for previous inconclusive attempts to compute solutions using Newton-Picard methods that are popular in the physical chemistry literature.
(Less)
- author
- Beardmore, R. E.
; Peplow, A. T.
LU
and Bresme, F.
- publishing date
- 2007
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Liquid phase, Ornstein-Zernike equation, Spinodal, Vapor phase
- in
- SIAM Journal on Scientific Computing
- volume
- 29
- issue
- 6
- pages
- 22 pages
- publisher
- Society for Industrial and Applied Mathematics
- external identifiers
-
- scopus:55549103717
- ISSN
- 1064-8275
- DOI
- 10.1137/060650659
- language
- English
- LU publication?
- no
- id
- 1162a66b-5f35-49bb-8d0a-595527d2739e
- date added to LUP
- 2021-02-15 19:53:17
- date last changed
- 2022-02-01 20:15:56
@article{1162a66b-5f35-49bb-8d0a-595527d2739e, abstract = {{<p>We study the codimension-one and -two bifurcations of the Ornstein-Zernike equation with hypernetted chain (HNC) closure with Lennard-Jones intermolecular interaction potential. The main purpose of the paper is to present the results of a numerical study undertaken using a suite of algorithms implemented in MATLAB and based on pseudo arc-length continuation for the codimension-one case and a Newton-GMRES method for the codimension-two case. Through careful consideration of the results of our computations, an argument is formulated which shows that spinodal isothermal solution branches arising in this model cannot be reproduced numerically. Furthermore, we show that the existence of an upper bound on the density that can be realized on a vapor isothermal solution branch, which must be present at a spinodal, causes the existence of at least one fold bifurcation along that vapor branch when density is used as the bifurcation parameter. This provides an explanation for previous inconclusive attempts to compute solutions using Newton-Picard methods that are popular in the physical chemistry literature.</p>}}, author = {{Beardmore, R. E. and Peplow, A. T. and Bresme, F.}}, issn = {{1064-8275}}, keywords = {{Liquid phase; Ornstein-Zernike equation; Spinodal; Vapor phase}}, language = {{eng}}, number = {{6}}, pages = {{2442--2463}}, publisher = {{Society for Industrial and Applied Mathematics}}, series = {{SIAM Journal on Scientific Computing}}, title = {{A numerical bifurcation analysis of the ornstein-zernike equation with hypernetted chain closure}}, url = {{http://dx.doi.org/10.1137/060650659}}, doi = {{10.1137/060650659}}, volume = {{29}}, year = {{2007}}, }