Emergent Many-body Interactions and Inapplicability of Hard Sphere Jamming Theory
- Datum: 29.05.2018
- Uhrzeit: 11:00 - 12:00
- Vortragende(r): Dr. Yoav G. Pollack
- Weizmann Institute of Science Rehovot, Israel
- Ort: Max-Planck-Institut für Dynamik und Selbstorganisation (MPIDS)
- Raum: SR 0.77
- Gastgeber: MPIDS
- Kontakt: golestanian-office@ds.mpg.de
The mechanism of jamming in soft matter was argued to be dimensionally independent in recent studies on hard spheres[1]. This curious claim comes from the surprising match between the scaling exponents of jamming predicted by the hard-sphere theory [2] and the numerical measurements in finite dimensions including 2D and 3D. Such a match seemingly suggests that the infinite-dimensional theory is applicable to realistic systems. Our current work addresses the puzzle of this lack of strong dimensional dependence usually observed in critical phenomena.
We study the jamming transition using effective inter-particle forces. In thermal materials where nevertheless the mean positions are well defined on a given time-scale, these effective forces are what keeps the particles ”in place”. We observe emergent effective many-body forces [3], and quantify them as a function of proximity to jamming. We conclude that for hard spheres the effective forces are binary precisely at jamming, and propose that this explains the match of theory and measurements. We further claim that the predictions of the infinite-dimensional theory of hard spheres should be inapplicable to more realistic particles which are never absolutely hard[4].
[1] For example: P. Charbonneau, J. Kurchan , G. Parisi, P. Urbani and F. Zamponi, Ann. Rev. Cond. Matt. Phys. 8 265-288 (2017).
[2] For example: A. Altieri , S. Franz, G. Parisi, Journal of Statistical Mechanics: Theory and Experiment, 2016 093301 (2016).
[3] O. Gendelman, E. Lerner, Y.G. Pollack, I. Procaccia, C. Rainone and B. Riechers, Phys. Rev. E 94, 051001(R) (2016).
[4] G. Parisi, Y.G. Pollack, I. Procaccia, C. Rainone and M. Singh, Submitted for publication (arXiv:1709.01607).
We study the jamming transition using effective inter-particle forces. In thermal materials where nevertheless the mean positions are well defined on a given time-scale, these effective forces are what keeps the particles ”in place”. We observe emergent effective many-body forces [3], and quantify them as a function of proximity to jamming. We conclude that for hard spheres the effective forces are binary precisely at jamming, and propose that this explains the match of theory and measurements. We further claim that the predictions of the infinite-dimensional theory of hard spheres should be inapplicable to more realistic particles which are never absolutely hard[4].
[1] For example: P. Charbonneau, J. Kurchan , G. Parisi, P. Urbani and F. Zamponi, Ann. Rev. Cond. Matt. Phys. 8 265-288 (2017).
[2] For example: A. Altieri , S. Franz, G. Parisi, Journal of Statistical Mechanics: Theory and Experiment, 2016 093301 (2016).
[3] O. Gendelman, E. Lerner, Y.G. Pollack, I. Procaccia, C. Rainone and B. Riechers, Phys. Rev. E 94, 051001(R) (2016).
[4] G. Parisi, Y.G. Pollack, I. Procaccia, C. Rainone and M. Singh, Submitted for publication (arXiv:1709.01607).