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Exploring the jamming transition over a wide range of critical densities
by Misaki Ozawa, Ludovic Berthier, Daniele Coslovich
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|Authors (as registered SciPost users):||Ludovic Berthier · Daniele Coslovich|
|Preprint Link:||http://arxiv.org/abs/1705.10156v1 (pdf)|
|Date submitted:||2017-05-30 02:00|
|Submitted by:||Coslovich, Daniele|
|Submitted to:||SciPost Physics|
We numerically study the jamming transition of polydisperse spheres in three dimensions. We use an efficient thermalisation algorithm for the equilibrium hard sphere fluid and generate amorphous jammed packings over a range of critical jamming densities that is about three times broader than in previous studies. This allows us to reexamine a wide range of structural properties characterizing the jamming transition. Both isostaticity and the critical behavior of the pair correlation function hold over the entire range of critical densities. At intermediate length scales, we find a weak, smooth increase of bond orientational order. By contrast, distorted icosahedral structures grow rapidly with increasing the volume fraction in both fluid and jammed states. Surprisingly, at large scale we observe that denser jammed states show stronger deviations from hyperuniformity, suggesting that the enhanced amorphous ordering inherited from the equilibrium fluid competes with, rather than enhances, hyperuniformity. Finally, finite size fluctuations of the critical jamming density are considerably suppressed in the denser jammed states, indicating an important change in the topography of the potential energy landscape. By considerably stretching the amplitude of the critical "J-line", our work disentangles physical properties at the contact scale that are associated with jamming criticality, from those occurring at larger length scales, which have a different nature.
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- Cite as: Anonymous, Report on arXiv:1705.10156v1, delivered 2017-07-11, doi: 10.21468/SciPost.Report.186
Overall, it is very interesting to see that the width of the J-line can be widened, using tailored distributions, with all the critical behaviour remaining intact. The attempt to characterise the structural properties of these jammed states at different scales is also worthwhile. Therefore, I think this is a useful contribution that should be eventually published.
1) The work is done for a specific distribution of particle sizes, with a specific width (polydispersity 23%). I would guess that this choice of the distribution helps in pushing the critical densities to higher values. Is that the case ? It would be illustrative to show the results for a few more polydispersities, may be at least one larger and one smaller to see how the range of the J-line is dependent on this, if at all. Some earlier work, from Wilding, Sollich and co-workers, have suggested that large polydispersities would result in fractionation at large densities. The authors should comment on this vis-a-vis the jammed states.
2) Section B is very sketchy. For completeness, the authors should plot the distribution of sizes and also demonstrate that they are sitting on the equilibrium line. Otherwise, readers have to wade through other papers to follow this. In fact, in that section there are not
sufficient references for the readers, even to guide them through it.
4) The authors themselves point out that the number of rattlers are fairly large in the most dense system. They also try to discuss the spatial organisation of these rattlers. For this some snapshots might help to get an idea of how the rattlers are spatially distributed for
the different J points achieved. Is there some pattern regarding which sizes, large or small, are becoming rattlers ?
5) The system sizes studied are not optimum to discuss about the low k behaviour in chi(k) and related signatures of or deviations from
hyperuniformity (Fig.7d). Please discuss/comment
6) The discussion on finite size effects should perhaps come earlier, probably after III. Better data is needed for phi_fluid=0.635, for
Each of the 5 points in the Report above requests some clarifications, additions and changes.
- Cite as: Anonymous, Report on arXiv:1705.10156v1, delivered 2017-07-10, doi: 10.21468/SciPost.Report.187
Great, concise, detailed and well-written and carried out study.
This paper surely should be published. I have mostly semantic and cosmetical
comments and questions - maybe some small misunderstandings. The only
three points (marked by *) where a little more discussion or even a bit more
work is needed are given below. Howver, even without much additional work
this paper can go to print after the following points are addressed in the new
(Comments are written in chronological order of sequentially reading the paper
from beginning to end. If one or the other statement is falsified later, it still indicates
a possibility to improve by clarifying at the point where my question came up.)
in the sentence “Both …” the use of critical behavior and critical densities is slightly confusing.
Does not one imply the other in different sequence? Pls rephrase. Or is it so clear that I dont
see it? The two times ‘critical’ is maybe too much.
the contact scale $k->\infty$ is maybe too much? Those short wavelengths, are they really existing
or do you just want to talk about a (decoupled) length-scale that is much smaller than particles.
Waves - mechanical ones - relate to momentum transpot on the length-scale of (2) particles still.
I thought. For radiation and fluid motion through particles, the gaps could be really active and
relevant while for heat'electric transport the contact deformation is, but not for mechanical/momentum
and mechanical energy transport. But maybe I am wrong. So drop the $\infty$, which is too strict
anyway, or better specify which waves are really at this short lenght-scale.
at ‘global scale’ k->0 it is not only fluctuations but moreover harmonic motions (low standard eigenmodes),
and it is always a finite system, so 'global’ is maybe too strong a word.
density fluctuations - is it only that?
I rather think what is relevant are the fluctuations of the density of the contact network (fabric
or just coordination number), which does exclude rattlers, since the latter entities (as well as “soft”
regions that are enclosed by stable loops) are important - especially at jamming.
Density itself displays notoriously little variation around the mean (if rattlers are included).
hard spheres configurations -> hard sphere configurations
keeping cryst. under control? - you mean largely avoiding larger crstalline regions?
And where does a local tetrahedron end and where does a crystal start?
* minute changes … I thought the protocol in  (overcompression) would not take very long to
generate a considerable J-range? and does not need orders of magnitude variation in time-scale
to generate some finite variation? (where the rather small range presented is due to absence
of friction). However, only later in the paper, it becomes clear that here it is also about frictionless
systems (state that earlier! e.g. in 1st line of abstract or even in the title?) so that indeed the
present system goes beyond the range in  which, however, was not exploring enormous
overcompression above volume-fraction 1 [which was done before, up to 10, but I dont find
back the reference]. Eventually the question remains, whether the presented results are not
due to the presently used procedure and how general that is. (I dont expect the authors to
have the answer, but the question should be raised at the end of the paper).
When I extrapolate Eq.(5) in Ref. up to vol.frac.=10, I also get very close to 0.7,
while the polydispersities are somewhat different in both cases, the lower end of the J-line
almost matches. Too bad that the authors in  have not done this, and the present authors
use a different method … however, I think it would not be a big deal for the present authors
to do an enormous over compression and return back below jamming to see where
the jamming point has moved. Notably the present work and the preparation (over-
compression) in  are both isotropic. So my question is whether the both methods
give the same structures of high-density jammed systems at the end.
in the procedure-section:
why are the displacements taken from a cube - I would rather take them from a sphere to
keep the displacements isotropic - which a cube might disturb?!
the fluid branc is explored up to 0.655, which sounds like contradictory to the wide
range up to 0.7 volume fraction that is mentioned in the previous intro section.
What I miss in the description II.B. is: how close are the fluid states to jamming (how big
are the gaps?)
In the caption of Fig.1 it says: ‘rapid compression’ but in II.C a up-down-method is
explained - which is true? Also it is not clear if the left point is the Poisson phi_J,
or if the dashed line? for which size?
* In Fig.3, while the gamma=0.5 with different offset/factor is well supported by the data,
I do not see a good support of the gamma=0.41269 - and surely not for more than 1 or
maximally 2 digits. Thus the universality argument I would buy for the 0.5, but surely
NOT for the other value (0.41269) It seems to hold indeed for the lower end, but not
for the upper end of the J-line :-(
Does the present structural order have something to do with the ‘fluid with solid
features’ and ‘solid with fluid features’ speculated about in ? Or is it about
both states having similar features? I am not sure that I understand.
What I miss in and around V.C is the analysis of the rattler sizes.
Are they take from the small fraction or randomly from all sizes of the distribution.
Furthermore a few snapshots of the rattler-clusters might be instructive?
And also, what is the volume fraction of rattlers, where a change in rattlers
volume fraction could indicate a change in contributions from different size
An hypothesis -> A hypothesis
* Discussion of the dynamic density fluctuations and the existence of rattler clusters
(related to the statement about density-fluctuations above) could profit from some
more in-depth study. Rattlers are (do they?) NOT participating in the dynamic
(harmonic?) oscillations of the mechanically stable network and thus could indeed
be the origin of the dens-fluct.?! I agree that rattlers are not the central origin,
but with them comes the question about their clustering and their sizes.
If their sizes change, the remaining stable network has a de-facto different
size-distribution. And with that it will have different low-eigenmodes and
eigen-mode-shapes?! This might be more related to the change in \xi
Fig.10: are the data with or without rattlers? Maybe I overlooked.
Concomitantly was a new word for me - is not there a better way to
The last paragraph in VI was highly speculative and incomplete. I am not
sure that it is a good ending of the otherwise very concise study. Either
I did not understand it, so pls. rephrase, or move it to conclusion and discussion.
Rattler-free packings could be obtained by growing ONLY the rattlers and NOT
by compressing the whole packing.
The icosahedra are distorted due to the size-distribution. True? then say this
clearly also in the conclusion so that it becomes more stand-alone.
The second-last sentence, could be a little more relating to the prediction in
121 and 122, where the equivalent packings to polydisperse packings were given
explicitly and - close to jamming - the importance of the rattlers contribution was
highlighted. Explicitly, the behavior of a multidisperse system and its equivalent
tridisperse system was found to be similar (under isotropic compression - shear
was not tested to my knowledge) if not identical - but ONLY after the rattlers were
removed from the size-distribution.
The authors might want to address more clearly in their conclusions the following issues,
either as an opinion or as a speculation (this is to the authors - I am curious about their
opinions on this.
Friction - does it matter or does it just move the J-line and its range. Does it add something
really new, or would it allow to explore jammed systems down to the transition density of ~0.53?
J-line finite size - make a more clear statement that the J-line is NOT a finite size effect
and that the finite size fluctuations have nothing to do with the protocol dependence
but rather smear it out and maybe hide it.
Shear-jamming: what would happen under shear?