Skip to Main Content

Access Provided by Xinjiang University

Physical Review E

Editors' Suggestion
Access by Xinjiang University

Hydrodynamics in kinetically constrained lattice-gas models

Eial Teomy^1,2,* and Yair Shokef^1,†

¹School of Mechanical Engineering and Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
²Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel

^*eialteom@gmail.com
^†shokef@tau.ac.il

Phys. Rev. E 95, 022124 – Published 21 February, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.022124

Abstract

Kinetically constrained models are lattice-gas models that are used for describing glassy systems. By construction, their equilibrium state is trivial and there are no equal-time correlations between the occupancy of different sites. We drive such models out of equilibrium by connecting them to two reservoirs of different densities, and we measure the response of the system to this perturbation. We find that under the proper coarse-graining, the behavior of these models may be expressed by a nonlinear diffusion equation, with a model- and density-dependent diffusion coefficient. We find a simple approximation for the diffusion coefficient, and we show that the relatively mild discrepancy between the approximation and our numerical results arises due to non-negligible correlations that appear as the system is driven out of equilibrium, even when the density gradient is infinitesimally small. Similar correlations appear when such kinetically constrained models are driven out of equilibrium by applying a uniform external force. We suggest that these correlations are the reason for the same discrepancy between the approximate diffusion coefficient and the numerical results for a broader group of models—nongradient lattice-gas models—for which kinetically constrained models are arguably the simplest example thereof.

Physics Subject Headings (PhySH)

Article Text

References (53)

F. Ritort and P. Sollich, Adv. Phys. 52, 219 (2003).
J. Garrahan, P. Sollich, and C. Toninelli, Dynamical Heterogeneities in Glasses, Colloids, and Granular Media, International Series of Monographs on Physics (Oxford University Press, Oxford, 2010).
L. Berthier and J. P. Garrahan, Phys. Rev. E 68, 041201 (2003).
D. Chandler, J. P. Garrahan, R. L. Jack, L. Maibaum, and A. C. Pan, Phys. Rev. E 74, 051501 (2006).
S. Léonard and P. Harrowell, J. Chem. Phys. 133, 244502 (2010).
R. Pastore, M. Ciamarra, and A. Coniglio, Fractals 21, 1350021 (2013).
R. Pastore, A. Coniglio, and M. Cimarra, Sci. Rep. 5, 11770 (2015).
J. P. Garrahan and D. Chandler, Phys. Rev. Lett. 89, 035704 (2002).
L. Berthier and J. Garrahan, J. Chem. Phys. 119, 4367 (2003).
E. Marinari and E. Pitard, Europhys. Lett. 69, 235 (2005).
S. Whitelam, L. Berthier, and J. P. Garrahan, Phys. Rev. E 71, 026128 (2005).
L. Berthier, G. Biroli, J. Bouchaud, W. Kob, K. Miyazaki, and D. Reichman, J. Chem. Phys. 126, 184504 (2007).
E. Teomy and Y. Shokef, Phys. Rev. E 92, 032133 (2015).
R. Pastore, A. de Candia, A. Fierro, M. Pica Ciamarra, and A. Coniglio, J. Stat. Mech.: Theor. Exp. (2016) 74011.
S. Butler and P. Harrowell, J. Chem. Phys. 95, 4454 (1991).
W. Kob and H. C. Andersen, Phys. Rev. E 48, 4364 (1993).
M. Einax and M. Schulz, J. Chem. Phys. 115, 2282 (2001).
M. Schulz and S. Trimper, J. Phys. Condens. Matter 14, 1437 (2002).
C. Kuhlmann, S. Trimper, and M. Schulz, Phys. Status Solidi B 242, 2401 (2005).
Y. Jung, J. Garrahan, and D. Chandler, J. Chem. Phys. 123, 084509 (2005).
J. Kurchan, L. Peliti, and M. Sellitto, Europhys. Lett. 39, 365 (1997).
S. Léonard, P. Mayer, P. Sollich, L. Berthier, and J. P. Garrahan, J. Stat. Mech.: Theor. Exp. (2007) P07017.
P. Mayer and P. Sollich, J. Phys. A 40, 5823 (2007).
C. Toninelli and G. Biroli, J. Stat. Phys. 130, 83 (2007).
G. Biroli and C. Toninelli, Eur. Phys. J. B 64, 567 (2008).
E. Teomy and Y. Shokef, Phys. Rev. E 86, 051133 (2012).
E. Teomy and Y. Shokef, Phys. Rev. E 89, 032204 (2014).
A. Ghosh, E. Teomy, and Y. Shokef, Europhys. Lett. 106, 16003 (2014).
F. Corberi and L. F. Cugliandolo, J. Stat. Mech.: Theor. Exp. (2009) P09015.
S. M. Fielding, Phys. Rev. E 66, 016103 (2002).
M. Sellitto, Phys. Rev. Lett. 101, 048301 (2008).
Y. Shokef and A. Liu, Europhys. Lett. 90, 26005 (2010).
F. Turci, E. Pitard, and M. Sellitto, Phys. Rev. E 86, 031112 (2012).
M. Sellitto, arXiv:astro-ph/9809186.
M. Sellitto, Phys. Rev. E 65, 020101 (2002).
M. Sellitto, J. Phys. Condens. Matter 14, 1455 (2002).
P. Gonçalves, C. Landim, and C. Toninelli, Ann. Inst. Henri Poincare, Sect. B 45, 887 (2009).
A. Karabanov, D. Wiśniewski, I. Lesanovsky, and W. Köckenberger, Phys. Rev. Lett. 115, 020404 (2015).
F. Spitzer, Adv. Math. 5, 246 (1970).
C. Toninelli, G. Biroli, and D. S. Fisher, Phys. Rev. Lett. 92, 185504 (2004).
E. Teomy and Y. Shokef, J. Chem. Phys. 141, 064110 (2014).
A. Lazarescu and K. Mallick, J. Phys. A 44, 315001 (2011).
C. Arita, P. L. Krapivsky, and K. Mallick, Phys. Rev. E 90, 052108 (2014).
C. Arita, P. Krapivsky, and K. Mallick, arXiv:1611.07719.
K. Nakazato and K. Kitahara, Prog. Theor. Phys. 64, 2261 (1980).
C. Toninelli, Ph.D. thesis, La Sapienza University, Italy, 2003.
A. Holroyd, Probab. Theor. Relat. Fields 125, 195 (2003).
E. W. Weisstein, Incomplete Beta Function. From MathWorld—A Wolfram Web Resource, http://mathworld.wolfram.com/IncompleteBetaFunction.html.
A. Aminov, Y. Kafri, and M. Kardar, Phys. Rev. Lett. 114, 230602 (2015).
B. Derrida, M. Evans, V. Hakim, and V. Pasquier, J. Phys. A 26, 1493 (1993).
P. L. Krapivsky and B. Meerson, Phys. Rev. E 86, 031106 (2012).
N. Segall, E. Teomy, and Y. Shokef, J. Stat. Mech.: Theor. Exp. (2016) 054051.
A. Kolomeisky, G. Schutz, E. Kolomeisky, and J. Straley, J. Phys. A 31, 6911 (1998).