Ref HAL: hal-00012892_v1
Ref Arxiv: cond-mat/0408694
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé:

We derive a dynamic field theory for a kinetically constrained model, based on the Fredrickson--Andersen model, which we expect to describe the properties of an Arrhenius (strong) supercooled liquid at the coarse-grained level. We study this field theory using the renormalization group. For mesoscopic length and time scales, and for space dimension d \\geq 2, the behaviour of the model is governed by a zero-temperature dynamical critical point in the directed percolation universality class. We argue that in d=1 its behaviour is that of compact directed percolation. We perform detailed numerical simulations of the corresponding Fredrickson-Andersen model on the lattice in various dimensions, and find reasonable quantitative agreement with the field theory predictions.

Ref HAL: hal-00023274_v1
Ref Arxiv: cond-mat/0412158
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé:

We compute analytically and numerically the four-point correlation function that characterizes non-trivial cooperative dynamics in glassy systems within several models of glasses: elasto-plastic deformations, mode-coupling theory (MCT), collectively rearranging regions (CRR), diffusing defects and kinetically constrained models (KCM). Some features of the four-point susceptibility chi_4(t) are expected to be universal. at short times we expect an elastic regime characterized by a t or sqrt{t} growth. We find both in the beta, and the early alpha regime that chi_4 sim t^mu, where mu is directly related to the mechanism responsible for relaxation. This regime ends when a maximum of chi_4 is reached at a time t=t^* of the order of the relaxation time of the system. This maximum is followed by a fast decay to zero at large times. The height of the maximum also follows a power-law, chi_4(t^*) sim t^{*lambda}. The value of the exponents mu and lambda allows one to distinguish between different mechanisms. For example, freely diffusing defects in d=3 lead to mu=2 and lambda=1, whereas the CRR scenario rather predicts either mu=1 or a logarithmic behaviour depending on the nature of the nucleation events, and a logarithmic behaviour of chi_4(t^*). MCT leads to mu=b and lambda =1/gamma, where b and gamma are the standard MCT exponents. We compare our theoretical results with numerical simulations on a Lennard-Jones and a soft-sphere system. Within the limited time-scales accessible to numerical simulations, we find that the exponent mu is rather small, mu < 1, with a value in reasonable agreement with the MCT predictions.

Commentaires: 26 pages, 6 figures

Résumé:

In a recent paper (Mayer et al, 2004 Phys. Rev. Lett. 93 115701) it was shown, by means of experiments, theory and simulations, that coarsening systems display dynamic heterogeneity analogous to that of glass formers. Here, we present a detailed analysis of dynamic heterogeneities in the Glauber-Ising chain. We discuss how dynamic heterogeneity in Ising systems must be measured through connected multi-point correlation functions. We show that in the coarsening regime of the Ising chain these multi-point functions reveal the growth of spatial correlations in the dynamics, beyond what can be inferred from standard two-point correlations. They have non-trivial scaling properties, which we interpret in terms of the diffusion-annihilation dynamics of domain walls. In the equilibrium dynamics of the Ising chain, on the other hand, connected multi-point functions vanish exactly and dynamic heterogeneity is not observed. We argue that the analysis of connected correlations in coarsening systems should help to explore similarities with the dynamics of glass formers.

Ref HAL: hal-00008334_v1
Ref Arxiv: cond-mat/0506629
DOI: 10.1088/0953-8984/17/45/050
WoS: 000235394200051
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
22 Citations
Résumé:

Kinetically constrained spin models are schematic coarse-grained models for the glass transition which represent an efficient theoretical tool to study detailed spatio-temporal aspects of dynamic heterogeneity in supercooled liquids. Here, we study how spatially correlated dynamic domains evolve with time and compare our results to various experimental and numerical investigations. We find that strong and fragile models yield different results. In particular, the lifetime of dynamic heterogeneity remains constant and roughly equal to the alpha relaxation time in strong models, while it increases more rapidly in fragile models when the glass transition is approached.

Commentaires: Submitted to the proceedings of the 6th EPS Liquid Matter Conference, Utrecht 2-6 July 2005

Résumé:

We suggest the emergence of spatially correlated dynamics in slowly compacting dense granular media by analyzing analytically and numerically multipoint correlation functions in a simple particle model characterized by slow nonequilibrium dynamics. We show that the logarithmically slow dynamics at large times is accompanied by spatially extended dynamic structures that resemble the ones observed in glass-forming liquids and dense colloidal suspensions. This suggests that dynamic heterogeneity is another key common feature present in very different jamming materials.

Résumé:

We study static and dynamic spatial correlations in a two-dimensional spin model with four-body plaquette interactions and standard Glauber dynamics by means of analytic arguments and Monte Carlo simulations. We study in detail the dynamical behavior which becomes glassy at low temperatures, due to the emergence of effective kinetic constraints in a dual representation where spins are mapped to plaquette variables. We study the interplay between nontrivial static correlations of the spins and the dynamic "four-point" correlations usually studied in the context of supercooled liquids. We show that slow dynamics is spatially heterogeneous due to the presence of diverging length scales and scaling, as is also found in kinetically constrained models. This analogy is illustrated by a comparative study of a froth model where the kinetic constraints are imposed.

DOI: 10.1088/0953-8984/17/45/046
WoS: 000235394200047
39 Citations
Résumé:

We study the dynamic behaviour of concentrated colloidal hard spheres using time resolved correlation, a light scattering technique that can detect the slow evolution of the dynamics in out-of-equilibrium systems. Surprisingly, equilibrium is reached a very loner time after sample initialization. the nonstationary regime lasting up to three orders of magnitude more than the relaxation time of the system. Before reaching equilibrium, the system displays unusual ageing behaviour. The intermediate scattering function decays faster than exponentially and its relaxation time evolves non-monotonically with sample age