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Register a new userCompetition and cooperation:aspects of dynamics in sandpiles
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In this article, we review some of our approaches to granular dynamics, now well known to consist of both fast and slow relaxational processes. In the first case, grains typically compete with each other, while in the second, they cooperate. A typical result of {it cooperation} is the formation of stable bridges, signatures of spatiotemporal inhomogeneities; we review their geometrical characteristics and compare theoretical results with those of independent simulations. {it Cooperative} excitations due to local density fluctuations are also responsible for relaxation at the angle of repose; the {it competition} between these fluctuations and external driving forces, can, on the other hand, result in a (rare) collapse of the sandpile to the horizontal. Both these features are present in a theory reviewed here. An arena where the effects of cooperation versus competition are felt most keenly is granular compaction; we review here a random graph model, where three-spin interactions are used to model compaction under tapping. The compaction curve shows distinct regions where fast and slow dynamics apply, separated by what we have called the {it single-particle relaxation threshold}. In the final section of this paper, we explore the effect of shape -- jagged vs. regular -- on the compaction of packings near their jamming limit. One of our major results is an entropic landscape that, while microscopically rough, manifests {it Edwards flatness} at a macroscopic level. Another major result is that of surface intermittency under low-intensity shaking.
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In a previous paper [Phys. Rev. Lett. 91, 014501 (2003)], the mechanism of revolving rivers for sandpile formation is reported: as a steady stream of dry sand is poured onto a horizontal surface, a pile forms which has a river of sand on one side owing from the apex of the pile to the edge of the base. For small piles the river is steady, or continuous. For larger piles, it becomes intermittent. In this paper we establish experimentally the dynamical phase diagram of the continuous and intermittent regimes, and give further details of the piles topography, improving the previous kinematic model to describe it and shedding further light on the mechanisms of river formation. Based on experiments in Hele-Shaw cells, we also propose that a simple dimensionality reduction argument can explain the transition between the continuous and intermittent dynamics.
We discuss the distribution of ions around highly charged PEs when there is competition between monovalent and multivalent ions, pointing out that in this case the number of condensed ions is sensitive to short-range interactions, salt, and model-dependent approximations. This sensitivity is discussed in the context of recent experiments on DNA aggregation, induced by multivalent counterions such as spermine and spermidine.
Using cyclic shear to drive a two dimensional granular system, we determine the structural characteristics for different inter-particle friction coefficients. These characteristics are the result of a competition between mechanical stability and entropy, with the latters effect increasing with friction. We show that a parameter-free maximum-entropy argument alone predicts an exponential cell order distribution, with excellent agreement with the experimental observation. We show that friction only tunes the mean cell order and, consequently, the exponential decay rate and the packing fraction. We further show that cells, which can be very large in such systems, are short-lived, implying that our systems are liquid-like rather than glassy.
The problem of the helix-coil transition of biopolymers in explicit solvents, like water, with the ability for hydrogen bonding with solvent is addressed analytically using a suitably modified version of the Generalized Model of Polypeptide Chains. Besides the regular helix-coil transition, an additional coil-helix or reentrant transition is also found at lower temperatures. The reentrant transition arises due to competition between polymer-polymer and polymer-water hydrogen bonds. The balance between the two types of hydrogen bonding can be shifted to either direction through changes not only in temperature, but also by pressure, mechanical force, osmotic stress or other external influences. Both polypeptides and polynucleotides are considered within a unified formalism. Our approach provides an explanation of the experimental difficulty of observing the reentrant transition with pressure; and underscores the advantage of pulling experiments for studies of DNA. Results are discussed and compared with those reported in a number of recent publications with which a significant level of agreement is obtained.
The dynamical arrest of gels is the consequence of a well defined structural phase transition, leading to the formation of a spanning cluster of bonded particles. The dynamical glass transition, instead, is not accompanied by any clear structural signature. Nevertheless, both transitions are characterized by the emergence of dynamical heterogeneities. Reviewing recent results from numerical simulations, we discuss the behavior of dynamical heterogeneities in different systems and show that a clear connection with the structure exists in the case of gels. The emerging picture may be also relevant for the more elusive case of glasses. We show, as an example, that the relaxation process of a simple glass-forming model can be related to a reverse percolation transition and discuss further perspective in this direction.
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