Analytic study of clustering in shaken granular material using zero-range processes

Török, János

doi:10.1016/j.physa.2005.03.024

Cited by 37 publications

(36 citation statements)

References 14 publications

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“…For example, a stretched exponential f (m) ∼ exp(−am α ) with α < 1 or a power law f (m) ∼ A/m b with b > 2 fulfils (3). The ensuing condensation which occurs will be referred to as standard condensation.…”

Section: Introductionmentioning

confidence: 99%

Condensation transition in joint large deviations of linear statistics

Szavits-Nossan¹,

Evans²,

Majumdar³

2014

J. Phys. A: Math. Theor.

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Abstract. Real space condensation is known to occur in stochastic models of mass transport in the regime in which the globally conserved mass density is greater than a critical value. It has been shown within models with factorised stationary states that the condensation can be understood in terms of sums of independent and identically distributed random variables: these exhibit condensation when they are conditioned to a large deviation of their sum. It is well understood that the condensation, whereby one of the random variables contributes a finite fraction to the sum, occurs only if the underlying probability distribution (modulo exponential) is heavy-tailed, i.e. decaying slower than exponential. Here we study a similar phenomenon in which condensation is exhibited for non-heavy-tailed distributions, provided random variables are additionally conditioned on a large deviation of certain linear statistics. We provide a detailed theoretical analysis explaining the phenomenon, which is supported by Monte Carlo simulations (for the case where the additional constraint is the sample variance) and demonstrated in several physical systems. Our results suggest that the condensation is a generic phenomenon that pertains to both typical and rare events.

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Section: Introductionmentioning

confidence: 99%

Condensation transition in joint large deviations of linear statistics

Szavits-Nossan¹,

Evans²,

Majumdar³

2014

J. Phys. A: Math. Theor.

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“…A similar phenomenon may occur in the clustering of compartmentalized shaken granular gasses. Under certain conditions condensation is observed, whereby most particles accumulate in one compartment [7,8].A paradigmatic model to study condensation in such nonequilibrium systems is the zero-range process (ZRP) [9,10]. In this model of mass transfer, particles hop between boxes with hopping rates uðnÞ which depend only on the occupation number n of the departing box.…”

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confidence: 99%

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confidence: 99%

Condensation in Temporally Correlated Zero-Range Dynamics

2009

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The impact of temporally correlated dynamics on nonequilibrium condensation is studied using a non-Markovian zero-range process (ZRP). We find that memory effects can modify the condensation scenario significantly: (i) For mean-field dynamics, the steady state corresponds to that of a Markovian ZRP, but with modified hopping rates which can affect condensation; (ii) for nearest-neighbor hopping dynamics in one dimension, the condensate is found to occupy two adjacent lattice sites and to drift with a finite velocity. The validity of these results in a more general context is discussed.

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“…Toy models, such as the ZRP, provide a theoretical foundation for understanding condensation in these systems. Exact results from the ZRP have also been used in models of vehicular traffic [1,24], reptation in polymer physics [25], and transport and coalescence in granular systems [26].…”

Section: Modelmentioning

confidence: 99%

Temporally correlated zero-range process with open boundaries: Steady state and fluctuations

2015

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We study an open-boundary version of the on-off zero-range process introduced in Hirschberg et al. [Phys. Rev. Lett. 103, 090602 (2009)]. This model includes temporal correlations which can promote the condensation of particles, a situation observed in real-world dynamics. We derive the exact solution for the steady state of the one-site system, as well as a mean-field approximation for larger one-dimensional lattices, and also explore the large deviation properties of the particle current. Analytical and numerical calculations show that, although the particle distribution is well described by an effective Markovian solution, the probability of rare currents differs from the memoryless case. In particular, we find evidence for a memory-induced dynamical phase transition.

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Analytic study of clustering in shaken granular material using zero-range processes

Cited by 37 publications

References 14 publications

Condensation transition in joint large deviations of linear statistics

Condensation transition in joint large deviations of linear statistics

Condensation in Temporally Correlated Zero-Range Dynamics

Temporally correlated zero-range process with open boundaries: Steady state and fluctuations

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