Inherent Structure Landscape Connection between Liquids, Granular Materials, and the Jamming Phase Diagram

Ashwin, Sarah; Yamchi, Mahdi Zaeifi; Bowles, Richard K.

doi:10.1103/physrevlett.110.145701

Cited by 36 publications

(41 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Clearly, we see that there is rich behavior to be found amidst the rattlerbackbone interactions in disordered, jammed sphere packings, highlighting the need for a statistical mechanical theory that is capable of accounting for such behavior. Moreover, understanding rattler phenomena in confined geometries [47] represents another fascinating area for future research.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Detailed characterization of rattlers in exactly isostatic, strictly jammed sphere packings

2013

View full text Add to dashboard Cite

We generate jammed disordered packings of 100≤N≤2000 monodisperse hard spheres in three dimensions whose strictly jammed backbones are demonstrated to be exactly isostatic with unprecedented numerical accuracy. This is accomplished by using the Torquato-Jiao (TJ) packing algorithm as a means of studying the maximally random jammed (MRJ) state. The rattler fraction of these packings converges towards 0.015 in the infinite-system limit, which is markedly lower than previous estimates for the MRJ state using the Lubachevsky-Stillinger protocol. This is because the packings that the TJ algorithm creates are closer to the true MRJ state, as shown using bond-orientational and translational order metrics. The rattler pair correlation statistics exhibit strongly correlated behavior contrary to the conventional understanding that they be randomly (Poisson) distributed. Dynamically interacting "polyrattlers" may be found imprisoned in shared cages as well as interacting through "bottlenecks" in the backbone and these clusters are mainly responsible for the sharp increase in the rattler pair correlation function near contact. We discover the surprising existence of polyrattlers with cluster sizes of up to five rattlers (which is expected to increase with system size) and present a distribution of polyrattler occurrence as a function of cluster size and system size. We also enumerate all of the rattler interaction topologies we observe and present images of several examples, showing that MRJ packings of monodisperse spheres can contain large rattler cages while still obeying the strict jamming criterion. The backbone spheres that encage the rattlers are significantly hypostatic, implying that correspondingly hyperstatic regions must exist elsewhere in these isostatic packings. We also observe that rattlers in hard-sphere packings share an apparent connection with the low-temperature two-level system anomalies that appear in real amorphous insulators and semiconductors.

show abstract

Section: Conclusion and Discussionmentioning

confidence: 99%

Detailed characterization of rattlers in exactly isostatic, strictly jammed sphere packings

2013

View full text Add to dashboard Cite

show abstract

“…It has been frequently observed that disks moving in a narrow channel can provide useful insights into glassy behavior [1][2][3][4][5][6][7]. In a recent paper [6] two of us studied the static and dynamic properties of N disks of diameter σ, which move in a narrow channel consisting of two impenetrable walls (lines) spaced by a distance H d , such that 1 < H d /σ < 1 + √ 3/2 (see Fig.…”

Section: Introductionmentioning

confidence: 99%

“…This number is readily determined in numerical work using the procedure given in Ref. [3]. Figure 11 shows θ as a function of packing fraction φ obtained from the simulations and compared with the analytical approach of Ref.…”

mentioning

confidence: 99%

Glasslike behavior of a hard-disk fluid confined to a narrow channel

2016

View full text Add to dashboard Cite

Disks moving in a narrow channel have many features in common with the glassy behavior of hard spheres in three dimensions. In this paper we study the caging behavior of the disks which sets in at characteristic packing fraction φ d . Four-point overlap functions similar to those studied when investigating dynamical heterogeneities have been determined from event driven molecular dynamics simulations and the time dependent dynamical length scale has been extracted from them. The dynamical length scale increases with time and, on the equilibration time scale, it is proportional to the static length scale associated with the zigzag ordering in the system, which grows rapidly above φ d . The structural features responsible for the onset of caging and the glassy behavior are easy to identify as they show up in the structure factor, which we have determined exactly from the transfer matrix approach.

show abstract

“…In the NN model, the dynamics becomes activated around a packing fraction φ d > 0.48 [1][2][3][4][5]. This is due to the onset of caging, a feature connected with the growth of a particular structural feature, zigzag order [1,2].…”

Section: Introductionmentioning

confidence: 99%

Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel

Godfrey

Moore

2015

Phys. Rev. E

View full text Add to dashboard Cite

We use an exact transfer-matrix approach to compute the equilibrium properties of a system of hard disks of diameter σ confined to a two-dimensional channel of width 1.95 σ at constant longitudinal applied force. At this channel width, which is sufficient for next-nearest-neighbor disks to interact, the system is known to have a great many jammed states. Our calculations show that the longitudinal force (pressure) extrapolates to infinity at a well-defined packing fraction φK that is less than the maximum possible φmax, the latter corresponding to a buckled crystal. In this quasi-onedimensional problem there is no question of there being any real divergence of the pressure at φK . We give arguments that this avoided phase transition is a structural feature -the remnant in our narrow channel system of the hexatic to crystal transition -but that it has the phenomenology of the (avoided) ideal glass transition. We identify a length scaleξ3 as our equivalent of the penetration length for amorphous order: In the channel system, it reaches a maximum value of around 15 σ at φK , which is larger than the penetration lengths that have been reported for three dimensional systems. It is argued that the α-relaxation time would appear on extrapolation to diverge in a Vogel-Fulcher manner as the packing fraction approaches φK .

show abstract

Inherent Structure Landscape Connection between Liquids, Granular Materials, and the Jamming Phase Diagram

Cited by 36 publications

References 51 publications

Detailed characterization of rattlers in exactly isostatic, strictly jammed sphere packings

Detailed characterization of rattlers in exactly isostatic, strictly jammed sphere packings

Glasslike behavior of a hard-disk fluid confined to a narrow channel

Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel

Contact Info

Product

Resources

About