Dynamical first-order phase transition in kinetically constrained models of glasses

We show that the dynamics of kinetically constrained models of glass formers takes place at a first-order coexistence line between active and inactive dynamical phases. We prove this by computing the large-deviation functions of suitable space-time observables, such as the number of configuration changes in a trajectory. We present analytic results for dynamic facilitated models in a mean-field approximation, and numerical results for the Fredrickson-Andersen model, the East model, and constrained lattice gases, in various dimensions. This dynamical first-order transition is generic in kinetically constrained models, and we expect it to be present in systems with fully jammed states.     

Traffic flow of mobile objects through obstacles: Turning and translational objects

We study the unidirectional flow of mobile objects through obstacles on a square lattice. Two models are presented: one is the lattice gas model consisting of translational particles and the other is that of turning particles. Fundamental diagrams for the two models are presented. The traffic flow of translational particles is compared with that of turning particles. In the traffic flow of translational particles, the fundamental diagram shows a trapezoid shape in the random configuration of obstacles, while it shows a parabolic shape in the periodic configuration of obstacles. The traffic flow of turning particles with a back step shows a similar behavior to that of translational particles. In the traffic flow of turning particles without backward moves, the current becomes zero when the density is higher than a critical density. In the traffic flow of turning particles without a back step, the dynamical transition between free traffic and a perfectly jammed state occurs at the critical density, while dynamical transition does not occur in traffic flow of translational particles.     

Finite-size scaling analysis of the glass transition

We show that finite-size scaling techniques can be employed to study the glass transition. Our results follow from the postulate of a diverging dynamical correlation length at the glass transition whose physical manifestation is the presence of dynamical heterogeneities. We introduce a parameter B(T,L) whose temperature, T, and system size, L, dependences permit a precise location of the glass transition. We discuss the finite-size scaling behavior of a diverging susceptibility chi(L,T). These new techniques are successfully used to study two lattice models. The analysis straightforwardly applies to any glass-forming system.     

Liquid-glass transition of a fluid confined in a disordered porous matrix: a mode-coupling theory

We derive an extension of the mode-coupling theory for the liquid-glass transition to a class of models of confined fluids, where the fluid particles evolve in a disordered array of interaction sites. We find that the corresponding equations are similar to those describing the bulk, implying that the methods of investigation which were developed there are directly transferable to this new domain of application. We then compute the dynamical phase diagram of a simple model system and show that new and nontrivial transition scenarios, including reentrant glass transitions and higher-order singularities, can be predicted from the proposed theory.     

Jamming of packings of frictionless particles with and without shear

By minimizing the enthalpy of packings of frictionless particles, we obtain jammed solids at desired pressures and hence investigate the jamming transition with and without shear. Typical scaling relations of the jamming transition are recovered in both cases. In contrast to systems without shear, shear-driven jamming transition occurs at a higher packing fraction and the jammed solids are more rigid with an anisotropic force network. Furthermore, by introducing the macrofriction coefficient, we propose an explanation of the packing fraction gap between sheared and non-sheared systems at fixed pressure.     

On the Dynamics of the Glass Transition on Bethe Lattices

The Glauber dynamics of disordered spin models with multi-spin interactions on sparse random graphs (Bethe lattices) is investigated. Such models undergo a dynamical glass transition upon decreasing the temperature or increasing the degree of constrainedness. Our analysis is based upon a detailed study of large scale rearrangements which control the slow dynamics of the system close to the dynamical transition. Particular attention is devoted to the neighborhood of a zero temperature tricritical point. Both the approach and several key results are conjectured to be valid in a considerably more general context. PACS Numbers:75.50.Lk (Spin glasses), 64.70.Pf (Glass transitions), 89.20.Ff (Computer science     

Jamming Percolation and Glassy Dynamics

We present a detailed physical analysis of the dynamical glass-jamming transition which occurs for the so called Knight models recently introduced and analyzed in a joint work with D.S. Fisher (Toninelli et al., Phys. Rev. Lett. 96, 035702, 2006). Furthermore, we review some of our previous works on Kinetically Constrained Models. The Knight models correspond to a new class of kinetically constrained models which provide the first example of finite dimensional models with an ideal glass-jamming transition. This is due to the underlying percolation transition of particles which are mutually blocked by the constraints. This jamming percolation has unconventional features: it is discontinuous (i.e. the percolating cluster is compact at the transition) and the typical size of the clusters diverges faster than any power law when ρ ↗ ρ _c . These properties give rise for Knight models to an ergodicity breaking transition at ρ _c : at and above ρ _c a finite fraction of the system is frozen. In turn, this finite jump in the density of frozen sites leads to a two step relaxation for dynamic correlations in the unjammed phase, analogous to that of glass forming liquids. Also, due to the faster than power law divergence of the dynamical correlation length, relaxation times diverge in a way similar to the Vogel-Fulcher law.     

Experimental evidence for interplay of dynamic heterogeneity and finite-size effect in glassy polymers

Despite two decades of extensive research, direct experimental evidence of a dynamical length scale determining the glass transition of confined polymers has yet to emerge. Using a recently established experimental technique of interface micro-rheology we provide evidence of finite-size effect truncating the growth of a quantity proportional to a dynamical length scale in confined glassy polymers, on cooling towards the glass transition temperature. We show how the interplay of variation of polymer film thickness and this temperature-dependent growing dynamical length scale determines the glass transition temperature, which in our case of 2–3 nm thick films, is reduced significantly as compared to their bulk values.     

Universality in lattice models of dynamic arrest: introduction of an order parameter

We introduce an order parameter for dynamical arrest. Dynamically available volume (unoccupied space that is available to the motion of particles) is expressed as holes for the simple lattice models we study. Near the arrest transition the system is dilute in holes, so we expand dynamical quantities in a series of hole density. Unlike the situation when presented in particle density, all cases of simple models that we examine have a quadratic dependence of the diffusion constant on hole density. This observation implies that in certain regimes ideal dynamical arrest transitions may possess a hitherto unnoticed degree of universality.     

Phase Transitions in Traffic Models

It is suggested that the question of existence of a jamming phase transition in a broad class of single-lane cellular-automaton traffic models may be studied using a correspondence to the asymmetric chipping model. In models where such correspondence is applicable, jamming phase transition does not take place. Rather, the system exhibits a smooth crossover between free-flow and jammed states, as the car density is increased.     

Order-to-disorder transition in ring-shaped colloidal stains

A colloidal dispersion droplet evaporating from a surface, such as a drying coffee drop, leaves a distinct ring-shaped stain. Although this mechanism is frequently used for particle self-assembly, the conditions for crystallization have remained unclear. Our experiments with monodisperse colloidal particles reveal a structural transition in the stain, from ordered crystals to disordered packings. We show that this sharp transition originates from a temporal singularity of the flow velocity inside the evaporating droplet at the end of its life. When the deposition speed is low, particles have time to arrange by Brownian motion, while at the end, high-speed particles are jammed into a disordered phase.     

Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems

We show how dynamical heterogeneities in glass forming systems emerge as a consequence of the existence of dynamical constraints, and we offer an interpretation of the glass transition as an entropy crisis in trajectory space (space-time) rather than in configuration space. To illustrate our general ideas, we analyze the one-dimensional (d = 1) Fredrickson-Andersen and East models. Dynamics of such dynamically constrained systems are shown to be isomorphic to the statics of ( d + 1)-dimensional dense mixtures of polydisperse noninterpenetrating domains. The domains coincide with arrested regions in trajectory space.     

Second-order phase transition in two-dimensional cellular automaton model of traffic flow containing road sections

Two-dimensional cellular automaton model has been broadly researched for traffic flow, as it reveals the main characteristics of the traffic networks in cities. Based on the BML models, a first-order phase transition occurs between the low-density moving phase in which all cars move at maximal speed and the high-density jammed phase in which all cars are stopped. However, it is not a physical result of a realistic system. We propose a new traffic rule in a two-dimensional traffic flow model containing road sections, which reflects that a car cannot enter into a road crossing if the road section in front of the crossing is occupied by another car. The simulation results reveal a second-order phase transition that separates the free flow phase from the jammed phase. In this way the system will not be entirely jammed (“don’t block the box” as in New York City).     

Do binary hard disks exhibit an ideal glass transition?

We demonstrate that there is no ideal glass transition in a binary hard-disk mixture by explicitly constructing an exponential number of jammed packings with densities spanning the spectrum from the accepted amorphous glassy state to the phase-separated crystal. Thus the configurational entropy cannot be zero for an ideal amorphous glass, presumed distinct from the crystal in numerous theoretical and numerical estimates in the literature. This objection parallels our previous critique of the idea that there is a most-dense random (close) packing for hard spheres [Torquato, Phys. Rev. Lett. 84, 2064 (2000)10.1103/PhysRevLett.84.2064].     

Mechanical, vibrational, and dynamical properties of amorphous systems near jamming

Amorphous systems undergo the jamming transition when the density increases, temperature drops, or external shear stress decreases, as described by the jamming phase diagram which was proposed to unify different processes such as the glass transition, random close packing, and yielding under shear stress. At zero temperature and shear stress, the jamming transition occurs at a critical density at Point J. In this paper, we review recent studies of the material properties of marginally jammed solids and the glassy dynamics in the vicinity of Point J. As the only singular point in the jamming phase diagram, Point J exhibits special criticality in both mechanical and vibrational quantities. Dynamics approaching the glass transition in the vicinity of Point J show critical scalings, suggesting that the molecular glass transition and the colloidal glass transition are equivalent in the hard sphere limit. All these studies shed light on the long-standing puzzles of the glass transition and unusual properties of amorphous solids.     

Rheology of sheared monodisperse granular suspensions

Sheared granular suspensions can either flow or be jammed. They show as well a ‘melting’ transition: partially ordered flowing states are found which can be melted into fully disordered arrangements of grains by sufficient shear. While these are well documented phenomena, the underlying mechanisms and their control parameters are still far from clear. Via Molecular Dynamics simulations, we study the rheology of a model system of sheared frictional monodisperse granular materials [7, 8]. In particular, we aim to understand the nature of a critical line separating crystallised and melted states and the “jammed” region in the phase diagram. We outline as well connections and differences with thermal glass formers and colloidal suspensions.     

Microscopic mean-field theory of the jamming transition

Dense particle packings acquire rigidity through a nonequilibrium jamming transition commonly observed in materials from emulsions to sandpiles. We describe athermal packings and their observed geometric phase transitions by using equilibrium statistical mechanics and develop a fully microscopic, mean-field theory of the jamming transition for soft repulsive spherical particles. We derive analytically some of the scaling laws and exponents characterizing the transition and obtain new predictions for microscopic correlation functions of jammed states that are amenable to experimental verifications and whose accuracy we confirm by using computer simulations.     

Direct imaging of dynamical heterogeneities near the colloid-gel transition

We observe the microscopic dynamics of a suspension of colloids with attractive interaction by confocal fluorescence microscopy to provide a deeper understanding of the relationship between local structure and dynamics near the gel transition. We study the distinct and self-parts of the van Hove density-density correlation function applied to our experimental data. Separable fast and slow populations emerge in the self-part, while the distinct part shows a pronounced signature of dynamic heterogeneities close to the gel transition, dominated by the fast particles. The slow population close to the gel transition shares features with an attraction-driven colloidal glass, including a plateau in the mean squared displacement that provides an estimate for the dynamical localization length.     

Freezing transition in bi-directional CA model for facing pedestrian traffic

We present a bi-directional cellular automaton (CA) model for facing traffic of pedestrians on a wide passage. The excluded-volume effect and bi-directionality of facing traffic are taken into account. The CA model is not stochastic but deterministic. We study the jamming and freezing transitions when pedestrian density increases. We show that the dynamical phase transitions occur at three stages with increasing density. There exist four traffic states: the free traffic, jammed traffic 1, jammed traffic 2, and frozen state. At the frozen state, all pedestrians stop by preventing from going ahead each other. At three transitions, the pedestrian flow changes from the free traffic through the jammed traffic 1 and jammed traffic 2, to the frozen state.     

Shear-thickening and entropy-driven reentrance

We discuss a generic mechanism for shear thickening analogous to entropy-driven phase reentrance. We implement it in the context of nonrelaxational mean-field glassy systems: although very simple, the microscopic models we study present a dynamical phase diagram with second- and first-order stirring-induced jamming transitions leading to intermittency, metastability, and phase coexistence as seen in some experiments. The jammed state is fragile with respect to change in the stirring direction. Our approach provides a direct derivation of a mode-coupling theory of shear thickening.