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Density scaling of generalized Lennard-Jones fluids in different dimensions
by Thibaud Maimbourg, Jeppe C. Dyre, Lorenzo Costigliola
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Lorenzo Costigliola · Thibaud Maimbourg |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1912.08176v2 (pdf) |
| Date submitted: | June 9, 2020, 2 a.m. |
| Submitted by: | Lorenzo Costigliola |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Liquids displaying strong virial-potential energy correlations conform to an approximate density scaling of their structural and dynamical observables. These scaling properties do not extend to the entire phase diagram, in general. The validity of the scaling can be quantified by a correlation coefficient. In this work a simple scheme to predict the correlation coefficient and the density-scaling exponent is presented. Although this scheme is exact only in the dilute gas regime or in high dimension d, the comparison with results from molecular dynamics simulations in d = 1 to 4 shows that it reproduces well the behavior of generalized Lennard-Jones systems in a large portion of the fluid phase.
Current status:
Reports on this Submission
Report #2 by Daniele Coslovich (Referee 2) on 2020-7-10 (Invited Report)
- Cite as: Daniele Coslovich, Report on arXiv:1912.08176v2, delivered 2020-07-10, doi: 10.21468/SciPost.Report.1819
Strengths
- Solid theoretical and numerical work
- The derived analytical expressions may provide useful guidelines to simulations and experiments on dense liquids
Weaknesses
- Some parts of the presentation can be improved
Report
Requested changes
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I am not sure if this was discussed in some previous paper of the authors, but what is the physical interpretation of the peak in gamma(R)?
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p.11: "In 4d the system size is chosen to be the smallest necessary to reliably study the highest-density state points (ρ = 1.5)."
What kind of tests did the author perform to ensure this? Please mention it in the text.
- p.13 "Also, for d = 1, 2, 3 ordered phases are found at high densities for which the correlation coefficient R is almost unity."
Which points in the graph correspond to ordered states? It would be helpful to mark them somehow.
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fig.2 and 3 : the captions are pretty long; also part of the discussion in the caption would fit better in the main text
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fig.6a : y label should be gamma/gamma_peak
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fig.6: I think fig.6 should appear right after fig.2. Indeed, the discussion of fig.6 follows immediately the one of fig.2
Report #1 by Anonymous (Referee 1) on 2020-6-29 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1912.08176v2, delivered 2020-06-29, doi: 10.21468/SciPost.Report.1789
Strengths
1) This work further formalizes the theoretical context for the density scaling approach popularized by one of the co-authors. 2) The theory is assessed by a numerical study that takes the dimensional dependence into account.
Weaknesses
1) The organization of some of the figures does not always help with legibility.
Report
Requested changes
1) Presumably, the choice of normalization of Eq. (3) (to ensure "that the minimum does not shift when exponents vary") is made for some analytical or definitional convenience. Please specify.
2) Novel, dedicated figures should be included to enhance the discussion of Eqs (13) and (16). For instance, the mild dependence on n is not obvious to tease out from the equations alone. The non-trivial shape of the parametric temperature plot would also be more easily appreciated if it were presented separately. Panel (d) from Fig. 3 could additionally be included as part of this new presentation.
3) Figures should be discussed in the order in which they appear. A proposal: for ease of comparison, Figs 2 and 4 should appear side by side and the panels Fig. 6 might be included with those of Fig. 2.
4) The d=1 results could presumably also be approximated by a transfer matrix approach with next-nearest neighbour interactions, see, e.g., M. Godfrey and M. Moore, Phys. Rev. E 91, 022120 (2015). A note to this effect should be included.
5) On p. 11, the simulations are stated to be sufficiently long and sufficiently large for thermodynamic quantities to be accurately calculated. Are these estimates based on published data on quantitative convergence tests, or on length scale analysis? Additional details should be provided to motivate the "running time limitations".
Small correction: i) On p. 4, kB is set to unity, and the quantity is redefined on p. 6.