Geometry of dynamically available empty space is the key to near-arrest dynamics

Lawlor, Aonghus; Gregorio, Paolo De; Bradley, Phil; Sellitto, Mauro; Dawson, Kenneth A.

doi:10.1103/physreve.72.021401

Cited by 19 publications

(29 citation statements)

References 28 publications

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“…For each configuration, the arrows indicate allowed transitions (to be selected at random) involving the growth of one boundary line by one step. This process restores that local configuration to another intermediate state [P kϩ1,kϩs helpful in future formulations of quantitative laws for dynamical arrest also (34). The peak of the second derivative in Fig.…”

Section: Resultsmentioning

confidence: 99%

Exact solution of a jamming transition: Closed equations for a bootstrap percolation problem

Gregorio

Lawlor

Bradley

et al. 2005

Proc. Natl. Acad. Sci. U.S.A.

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Jamming, or dynamical arrest, is a transition at which many particles stop moving in a collective manner. In nature it is brought about by, for example, increasing the packing density, changing the interactions between particles, or otherwise restricting the local motion of the elements of the system. The onset of collectivity occurs because, when one particle is blocked, it may lead to the blocking of a neighbor. That particle may then block one of its neighbors, these effects propagating across some typical domain of size named the dynamical correlation length. When this length diverges, the system becomes immobile. Even where it is finite but large the dynamics is dramatically slowed. Such phenomena lead to glasses, gels, and other very long-lived nonequilibrium solids. The bootstrap percolation models are the simplest examples describing these spatio-temporal correlations. We have been able to solve one such model in two dimensions exactly, exhibiting the precise evolution of the jamming correlations on approach to arrest. We believe that the nature of these correlations and the method we devise to solve the problem are quite general. Both should be of considerable help in further developing this field.T here exists within nature a whole class of systems that exhibit a geometrical percolation transition at which they become spanned by a single infinite cluster extending across the whole system (1-3). Such transitions may be observed, for example, by randomly occupying lattice sites at some prescribed density. Spatio-temporal particle correlations implied by simple dynamical models may also be studied by using percolation ideas. Indeed, since its introduction (4, 5), the potential of the bootstrap percolation problem (6, 7) to analyze the dynamics of a system of highly coupled and locally interacting units has been recognized. The range of applications has continued to grow (8)(9)(10)(11)(12).This problem is of particular interest because of a growing focus on, and appreciation of, the unifying role of dynamical arrest (13-17) or jamming (18) in the formation of complex condensed states of matter. Despite many advances, there is as yet no complete and fundamental conceptual framework to describe the phenomena. In comparable situations it has been an important lesson of critical phenomena (19,20) that an exact solution, even of a 2D model system, can be of great assistance in broader efforts to understand the issues. Thus, an exact closed solution of one bootstrap problem (with all of the implications of strong packing-induced coupling and divergent correlated domains) would represent, even without direct access to transport coefficients, a solution of a nontrivial (and non-mean field) jamming or arrest scenario. We will present such a solution in this article.That such a treatment is possible must be considered surprising, for there have been no prior indications of such simplification, to our knowledge.The connection of the bootstrap percolation problem to jamming phenomena is clear. Thus, particles, process...

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Section: Resultsmentioning

confidence: 99%

Exact solution of a jamming transition: Closed equations for a bootstrap percolation problem

Gregorio

Lawlor

Bradley

et al. 2005

Proc. Natl. Acad. Sci. U.S.A.

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“…However, the range of time/density considered here is still small to resolve these different sectors. The distinction between connected and disconnected holes should also be made, as the former should be much more important in the compaction mechanism, along with the study of their spatial distribution [59]. Correlations may be also defined considering only the holes, with the associated dynamical susceptibility.…”

Section: Discussionmentioning

confidence: 99%

Heterogeneities in aging models of granular compaction

Arenzon¹

2006

Braz. J. Phys.

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Kinetically constrained models (KCM) are systems with trivial thermodynamics but often complex dynamical behavior due to constraints on the accessible paths followed by the system. Exploring these properties, the KobAndersen (KA) model was introduced to study the slow dynamics of glass forming liquids and later extended to granular materials. In this last context, we present new results on the heterogeneous character of both in and out of equilibrium dynamics, further stretching the granular-glass analogy.

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“…31 The Kob-Andersen model 3 correctly reproduces this intracage behavior of glassy systems, as well as many other important signatures such as blocked nonergodic states and dynamical heterogeneities. 18,19,32 Being a lattice gas at the equilibrium, this model does not present any ordered state or thermodynamic phase transition. Our aim, then, is to implement a similar kinetic rule in our model and study the interplay arising between arrest and crystallization.…”

Section: B the Kinetic Constraintmentioning

confidence: 99%

“…Kinetically constrained models, such as the one introduced by Kob and Andersen, 3 represent the intracage behavior of glassy systems on a lattice and produce blocked nonergodic states and dynamical heterogeneities. 18,19 Despite their success, such simple models are criticized because they have no energy relaxation, possess no underlying crystal phase, and fail to exhibit the correct decay of dynamical correlations with time. Experimental studies of glass transitions 1 are primarily presented with temperature as the control parameter, and the heat capacity plays a a) Author to whom correspondence should be addressed.…”

Section: Introductionmentioning

confidence: 99%

Lattice model of glasses

Cellai

Fima

Lawlor

et al. 2011

The Journal of Chemical Physics

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Glass-forming liquids have been extensively studied in recent decades, but there is still no theory that fully describes these systems, and the diversity of treatments is in itself a barrier to understanding. Here we introduce a new simple model that (possessing both liquid-crystal and glass transition) unifies different approaches, producing most of the phenomena associated with real glasses, without loss of the simplicity that theorists require. Within the model we calculate energy relaxation, nonexponential slowing phenomena, the Kauzmann temperature, and other classical signatures. Moreover, the model reproduces a subdiffusive exponent observed in experiments of dense systems. The simplicity of the model allows us to identify the microscopic origin of glassification, leaving open the possibility for theorists to make further progress.

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Geometry of dynamically available empty space is the key to near-arrest dynamics

Cited by 19 publications

References 28 publications

Exact solution of a jamming transition: Closed equations for a bootstrap percolation problem

Exact solution of a jamming transition: Closed equations for a bootstrap percolation problem

Heterogeneities in aging models of granular compaction

Lattice model of glasses

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