Density fluctuations in vibrated granular materials

Nowak, E. R.; Knight, James B.; Ben‐Naim, E.; Jaeger, Heinrich M.; Nagel, Sidney R.

doi:10.1103/physreve.57.1971

Cited by 486 publications

(662 citation statements)

References 23 publications

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“…Finally, once the system reaches its final state, density fluctuations can be measured and compared with Monte Carlo simulations of the parking process. Our preliminary results indicate that measured and simulated Power Spectrum Density (PSD) of the density fluctuations are strikingly similar [24]. The high frequency limit is Lorentzian (f −2 ), while the low density limit is white-noise (f 0 ).…”

mentioning

confidence: 89%

Slow relaxation in granular compaction

Ben‐Naim

Knight

Nowak

et al. 1998

Physica D: Nonlinear Phenomena

112

109

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Experimental studies show that the density of a vibrated granular material evolves from a low density initial state into a higher density final steady state. The relaxation towards the final density value follows an inverse logarithmic law. We propose a simple stochastic adsorption-desorption process which captures the essential mechanism underlying this remarkably slow relaxation. As the system approaches its final state, a growing number of beads have to be rearranged to enable a local density increase. In one dimension, this number grows as N = ρ/(1 − ρ), and the density increase rate is drastically reduced by a factor e −N . Consequently, a logarithmically slow approach to the final state is found ρ∞ − ρ(t) ∼ = 1/ ln t.

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mentioning

confidence: 89%

Slow relaxation in granular compaction

Ben‐Naim

Knight

Nowak

et al. 1998

Physica D: Nonlinear Phenomena

112

109

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“…As already mentioned, we will refer to a process as a "heating" ("cooling") one when the vibration intensity is monotonically increased (decreased). Such kind of processes have been already considered in the literature, both in real granular systems [2,3] and in simple models [19].…”

Section: Processes With Time-dependent Vibration Intensitymentioning

confidence: 99%

“…The transition rates W ij would be functions of the parameter Γ characterizing the strength of the vibration. If the granular pile is vibrated with sinusoidal pulses of amplitude A and frequency ω, the quantity Γ = Aω 2 /g [1,2], where g is the gravity, is usually defined. In the case of time dependent intensity Γ, the equation determining the evolution of the granular pile will be of the type given by Eq.…”

Section: Some General Dynamical Propertiesmentioning

confidence: 99%

“…Then, it seems worth studying its behavior when the tapping strength changes in time for several reasons. Firstly, in order to verify if its behavior resembles that of real granular systems, showing the irreversible and reversible branches found in experiments [2]. Secondly, to understand whether the hysteresis effects are related to the existence of a "normal solution" of the master equation with time-dependent tapping strength.…”

Section: Introductionmentioning

confidence: 99%

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Hysteresis in vibrated granular media

Prados

Brey

Sánchez-Rey

2000

Physica A: Statistical Mechanics and its Applications

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Some general dynamical properties of models for compaction of granular media based on master equations are analyzed. In particular, a one-dimensional lattice model with short-ranged dynamical constraints is considered. The stationary state is consistent with Edward's theory of powders. The system is submitted to processes in which the tapping strength is monotonically increased and decreased. In such processes the behavior of the model resembles the reversible-irreversible branches which have been recently observed in experiments. This behavior is understood in terms of the general dynamical properties of the model, and related to the hysteresis cycles exhibited by structural glasses in thermal cycles. The existence of a "normal" solution, i. e., a special solution of the master equation which is monotonically approached by all the other solutions, plays a fundamental role in the understanding of the hysteresis effects.

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“…a mechanical perturbation like tapping or shaking) must be comparable with the variation in potential energy required to rearrange the system structure. The process exhibits rather a rich behaviour with reversible and irreversible cycles as a function of the perturbation amplitude [9], and logarithmic [10] or stretched exponential laws [11] in the number of tapping.…”

Section: Models For Granularsmentioning

confidence: 99%

Lattice models of disorder with order

Petri¹

2003

Braz. J. Phys.

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This paper describes the use of simple lattice models for studying the properties of structurally disordered systems like glasses and granulates. The models considered have crystalline states as ground states, finite connectivity, and are not subject to constrained evolution rules. After a short review of some of these models, the paper discusses how two particularly simple kinds of models, the Potts model and the exclusion models, evolve after a quench at low temperature to glassy states rather than to crystalline states. I IntroductionIn recent years, there is growing interest in systems commonly found in disordered structural configurations such as glasses and dense granulates. Clearly different in many respects, these two classes of materials share in common the property of displaying stable states which are very far from what would be expected from equilibrium considerations [1,2]. As a consequence of this property other features emerge, like slow relaxation and response functions.Models of disorder are generally based on the presence of quenched, or a priori, disorder which takes the system far from ordered configurations. Only recently it has been observed that lattice models capable of ordering can also well reproduce many properties of disordered systems. On the other hand glass formers in nature usually have crystalline states as ground states, but this does not prevent them from being frequently found in some glassy state. The situation for a granular system is in general different, insofar as irregular grains inhibit the evolution of ordered states. Nevertheless even in the case of identical beads it is practically impossible to arrange them into an ordered fashion merely by supplying the energy to them.The aim of this paper is to briefly review some lattice models employed in the description of the slow dynamics of glasses and dense granular matter, which do not possess any a priori disorder nor long range interactions. We shall not discuss in detail the models, but just recall some of the main results, addressing the interested reader to the bibliography. More attention will be drawn to some recent observations regarding the condition for the emergence of glassy phases in some models of this kind.The paper is structured as follows: in Section II exclusion models and hard particle models are briefly introduced together with their employment in irreversible dynamics; Section III is devoted to their use in the description of dense granular matter and related results; Section IV describes spin models which have been recently shown to exhibit glassy states and associated slow dynamics; finally in Sec. V some new ideas are illustrated on when and why glassy states are generated in the place of crystalline states in some lattice models. II Exclusion and hard particle modelsFlory [3] modeled the irreversible deposition of dimers on a one-dimensional surface by the random sequential adsorption (RSA) of particles on a lattice. In this model, particles are placed one at time at randomly chosen positions of a ...

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Density fluctuations in vibrated granular materials

Cited by 486 publications

References 23 publications

Slow relaxation in granular compaction

Slow relaxation in granular compaction

Hysteresis in vibrated granular media

Lattice models of disorder with order

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