Jamming by shape in kinetically constrained models

Teomy, Eial; Shokef, Yair

doi:10.1103/physreve.89.032204

Cited by 10 publications

(21 citation statements)

References 62 publications

(116 reference statements)

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“…the particles are antipersistent). This correction to the base diffusion coefficient is qualitatively similar to the combined effect of persistence and finite density on the MSD, which increases with density for highly anti-persistent walkers [53]. Note that as this is not a gradient model, using the density dependence of the correlation functions at pseudo-equilibrium is only an approximation [58].…”

Section: Effective Diffusion Equationmentioning

confidence: 59%

“…In this paper we generalise our previous study [53] and consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a d dimensional hypercubic lattice. If the velocity autocorrelations are positive, we call the walkers persistent, while if they are negative we call them anti-persistent.…”

Section: Introductionmentioning

confidence: 99%

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Correlations and transport in exclusion processes with general finite memory

Teomy¹,

Metzler²

2019

J. Stat. Mech.

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We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a d dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical density. Above the critical density, the effective diffusion coefficient decreases with the particles' propensity to move forward and below the critical density it increases with their propensity to move forward. If the correlations are neglected the critical density is exactly 1/2. We also derive a low-density approximation for the same time correlations between different sites. We perform simulations on a one-dimensional system with one-step memory and find good agreement between our analytical derivation and the numerical results. We also consider the previously unexplored special case of totally anti-persistent particles. Generally, the correlation length converges to a finite value. However in the special case of totally anti-persistent particles and density 1/2, the correlation length diverges with time. Furthermore, connecting a system of totally anti-persistent particles to external particle reservoirs creates a new phenomenon: In almost all systems, regardless of the precise details of the microscopic dynamics, when a system is connected to a reservoir, the mean density of particle at the edge is the same as the reservoir following the zeroth law of thermodynamics. In a totally anti-persistent system, however, the density at the edge is always higher than in the reservoir. We find a qualitative description of this phenomenon which agrees reasonably well with the numerics.Correlations and transport in exclusion processes with general finite memory

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Section: Effective Diffusion Equationmentioning

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Correlations and transport in exclusion processes with general finite memory

Teomy¹,

Metzler²

2019

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Extending this algorithm to higher dimensional models with m = 2 is straightforward, since the unfrozen region must be a hyper-rhomboid, 25,26 such that at any stage in the algorithm the only variables which should be kept in memory are the size of the hyper-rhomboid (d variables, with d being the dimension of the system), the number of occupied checked sites in the two layers adjacent to each of the 2d sides (4d variables), and whether the corners are occupied or not (2 d variables), for a total of 2 d + 5d variables. For m ≥ 3, the extension of the algorithm is not trivial, since the unfrozen region does not have to be a hyper-rhomboid.…”

Section: Simulation Algorithmmentioning

confidence: 99%

“…These models can be expanded to higher dimensional hyper-cubic lattices with a general number m of vacant neighbors needed for movement. 25,26 We restrict ourselves in this article to the m = 2 models in a two-dimensional square lattice. Our work can be easily extended to higher dimensional models with a) eialteom@post.tau.ac.il b) shokef@tau.ac.il m = 2, but extending it to models with m ≥ 3 is much more complicated.…”

Section: Introductionmentioning

confidence: 99%

“…The behavior of finite-sized systems is interesting on its own right, 26 due to the finite extent of numerical simulations [28][29][30][31][32] but also because of the physical problem of jamming in confined geometries. 25,33,34 Instead of running the full physical dynamics of these models, a faster way to find n F is to run culling dynamics. In these dynamics the system is scanned iteratively, such that in each step the mobile particles are removed, until either all particles are removed or those remaining cannot be removed.…”

Section: Introductionmentioning

confidence: 99%

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Finite-density effects in the Fredrickson-Andersen and Kob-Andersen kinetically-constrained models

Teomy

Shokef

2014

The Journal of Chemical Physics

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We calculate the corrections to the thermodynamic limit of the critical density for jamming in the Kob-Andersen and Fredrickson-Andersen kinetically-constrained models, and find them to be finite-density corrections, and not finite-size corrections. We do this by introducing a new numerical algorithm, which requires negligible computer memory since contrary to alternative approaches, it generates at each point only the necessary data. The algorithm starts from a single unfrozen site and at each step randomly generates the neighbors of the unfrozen region and checks whether they are frozen or not. Our results correspond to systems of size greater than 10(7) × 10(7), much larger than any simulated before, and are consistent with the rigorous bounds on the asymptotic corrections. We also find that the average number of sites that seed a critical droplet is greater than 1.

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Motion of active tracer in a lattice gas with cross-shaped particles

Chatterjee

Segall

Merrigan

et al. 2019

The Journal of Chemical Physics

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We analyze the dynamics of an active tracer particle embedded in a thermal lattice gas. All particles are subject to exclusion up to third nearest neighbors on the square lattice, which leads to slow dynamics at high densities. For the case with no rotational diffusion of the tracer, we derive an analytical expression for the resulting drift velocity v of the tracer in terms of non-equilibrium density correlations involving the tracer particle and its neighbors, which we verify using numerical simulations. We show that the properties of the passive system alone do not adequately describe even this simple system of a single non-rotating active tracer. For large activity and low density, we develop an approximation for v. For the case where the tracer undergoes rotational diffusion independent of its neighbors, we relate its diffusion coefficient to the thermal diffusion coefficient and v. Finally we study dynamics where the rotation of the tracer is limited by the presence of neighboring particles. We find that the effect of this rotational locking may be quantitatively described in terms of a reduction of the rotation rate.

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Jamming by shape in kinetically constrained models

Cited by 10 publications

References 62 publications

Correlations and transport in exclusion processes with general finite memory

Correlations and transport in exclusion processes with general finite memory

Finite-density effects in the Fredrickson-Andersen and Kob-Andersen kinetically-constrained models

Motion of active tracer in a lattice gas with cross-shaped particles

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