We add relaxation mechanisms that mimic the effect of temperature and non-equilibrium driving to the recently-proposed spiral model which jams at a critical density rho_c < 1. This enables us to explore unjamming by temperature or driving at rho_c < rho < 1. We numerically calculate the relaxation time of the persistence function and its spatial heterogeneity. We disentangle the three different relaxation mechanisms responsible for unjamming when varying density, temperature, and driving strength, respectively. We show that the spatial scale of dynamic heterogeneity depends on density much more strongly than on temperature and driving.
Kinetically constrained spin models are known to exhibit dynamical behavior mimicking that of glass forming systems. They are often understood as coarse-grained models of glass formers, in terms of some "mobility" field. The identity of this "mobility" field has remained elusive due to the lack of coarse-graining procedures to obtain these models from a more microscopic point of view. Here we exhibit a scheme to map the dynamics of a two-dimensional soft disc glass former onto a kinetically constrained spin model, providing an attempt at bridging these two approaches.
We investigate a three-dimensional kinetically-constrained model that exhibits two types of phase transitions at different densities. At the jamming density $ ρ_J $ there is a mixed-order phase transition in which a finite fraction of the particles become frozen, but the other particles may still diffuse throughout the system. At the caging density $ ρ_C > ρ_J $, the mobile particles are trapped in finite cages and no longer diffuse. The caging transition occurs due to a percolation transition of the unfrozen sites, and we numerically find that it is a continuous transition with the same criti…
Kinetically constrained models (KCM) generically have trivial thermodynamics and yet manifest rich glassy dynamics. In order to resolve the thermodynamics-dynamics disconnect in KCMs, we derive a KCM by coarse-graining a non-trivial thermodynamic model with a solvable partition function. Blending of thermodynamics to the KCM makes the role of landscape properties on the relaxation times, fragility and its crossover analytically transparent. Using Bethe ansatz, we calculate the time-dependent $N$-point probability function in the distinct dynamical regimes of the landscapes; the contribution of…
Glasses prepared by physical vapour deposition have been shown to be remarkably more stable than those prepared by standard cooling protocols, with properties that appear to be similar to systems aged for extremely long times. When subjected to a rapid rise in temperature, ultrastable glasses anneal towards the liquid in a qualitatively different manner than ordinary glasses, with the seeming competition of different timescales and lengthscales. We numerically reproduce the phenomenology of ultrastable glass annealing with a kinetically constrained model, a three dimensional East model with so…
We add extreme driving to the Kob-Andersen kinetically-constrained lattice-gas model in order to mimic the effect of gravity on dense granular systems. For low particle densities, the current that develops in the system agrees at arbitrary field intensity with a mean field theory. At intermediate densities, spatial correlations give rise to non-monotonic dependence of the current on field intensity. At higher densities, the current ultimately vanishes at a finite, field-dependent jamming density. We supplement the study of this bulk behavior with an investigation of the current through a narro…
We study dynamical heterogeneity and glassy dynamics in a kinetically constrained lattice gas model which has both translational and rotational degrees of freedom. We find that the rotational diffusion constant tracks the structural relaxation time as density is increased whereas the translational diffusion constant exhibits a strong decoupling. We investigate distributions of exchange and persistence times for both the rotational and translational degrees of freedom and compare our results on the distributions of rotational exchange times to recent single molecule studies.
We study an attractive version of the East model using the real-space renormalization group (RG) introduced by Stella et al. The former is a kinetically constrained model with an Ising-like interaction between excitations, and shows striking agreement with the phenomonology of attractive colloidal systems. We find that the RG predicts two nonuniversal dynamic exponents, which suggests that in the out-of-equilibrium regime the model coarsens via a two-stage mechanism. We explain this mechanism physically, and verify this prediction numerically. In addition, we find that the characteristic relax…
The dynamical behaviours of a kinetically constrained spin model (Fredrickson-Andersen model) on a Bethe lattice are investigated by a perturbation analysis that provides exact final states above the nonergodic transition point. It is observed that the time-dependent solutions of the derived dynamical systems obtained by the perturbation analysis become systematically closer to the results obtained by Monte Carlo simulations as the order of a perturbation series is increased. This systematic perturbation analysis also clarifies the existence of a dynamical scaling law, which provides a implica…
We review the use of kinetically constrained models (KCMs) for the study of dynamics in glassy systems. The characteristic feature of KCMs is that they have trivial, often non-interacting, equilibrium behaviour but interesting slow dynamics due to restrictions on the allowed transitions between configurations. The basic question which KCMs ask is therefore how much glassy physics can be understood without an underlying ``equilibrium glass transition''. After a brief review of glassy phenomenology, we describe the main model classes, which include spin-facilitated (Ising) models, constrained la…
We study dynamical heterogeneity and growing dynamical lengthscales in two kinetically constrained models, namely, the one- and two-vacancy assisted triangular lattice gases. One of the models is a strong glassformer and the other is a fragile glassformer. Both exhibit heterogeneous dynamics with broadly distributed timescales as seen in the distribution of persistence times. We show that the Stokes-Einstein relation is violated, to a greater degree in the fragile glassformer, and show how this violation is related to dynamic heterogeneity. We extract dynamical lengthscales from structure fact…
We study condensation in one-dimensional transport models with a kinetic constraint. The kinetic constraint results in clustering of immobile vehicles; these clusters can grow to macroscopic condensates, indicating the onset of dynamic phase separation between free flowing and arrested traffic. We investigate analytically the conditions under which this occurs, and derive a necessary and sufficient criterion for phase separation. This criterion is applied to the well-known Nagel-Schreckenberg model of traffic flow to analytically investigate the existence of dynamic condensates. We find that t…
Complex fluids in shear flow and biased dynamics in crowded environments exhibit counterintuitive features which are difficult to address both at theoretical level and by molecular dynamic simulations. To understand some of these features we study a schematic model of highly viscous liquid, the 2D Kob-Andersen kinetically constrained model, driven into non-equilibrium steady states by a uniform non-Hamiltonian force. We present a detailed numerical analysis of the microscopic behavior of the model, including transversal and longitudinal spatial correlations and dynamic heterogeneities. In part…
We present Monte Carlo simulations in a modification of the north-or-east-or-front model recently investigated by Berthier and Garrahan [J. Phys. Chem. B 109, 3578 (2005)]. In this coarse-grained model for relaxation in supercooled liquids, the liquid structure is substituted by a three-dimensional array of cells. A spin variable is assigned to each cell, with values 0 or 1 denoting respectively unexcited and excited local states in a mobility field. Change in local mobility (spin flip) for a given cell is permitted according to kinetic constraints determined by the mobilities of neighboring c…
We study the dynamics of a single chain polymer confined to a two dimensional cell. We introduce a kinetically constrained lattice gas model that preserves the connectivity of the chain, and we use this kinetically constrained model to study the dynamics of the polymer at varying densities through Monte Carlo simulations. Even at densities close to the fully-packed configuration, we find that the monomers comprising the chain manage to diffuse around the box with a root mean square displacement of the order of the box dimensions over time scales for which the overall geometry of the polymer is…
Recent theoretical advances have led to the creation of a unified phase diagram for the thermal glass and athermal jamming transitions. This diagram makes clear that, while related, the mode-coupling---or dynamic---glass transition is distinct from the jamming transition, occurring at a finite temperature and significantly lower density than the jamming transition. Nonetheless, we demonstrate a pre-jamming transition in athermal frictionless spheres which occurs at the same density as the mode-coupling transition and is marked by percolating clusters of locally rigid particles. At this density…
We investigate the relaxation process and the dynamical heterogeneities of the kinetically constrained Kob--Anderson lattice glass model, and show that these are characterized by different timescales. The dynamics is well described within the diffusing defect paradigm, which suggest to relate the relaxation process to a reverse--percolation transition. This allows for a geometrical interpretation of the relaxation process, and of the different timescales.
