An Automata Model of Granular Materials

Gutt, Gary; Haff, P. K.

doi:10.1109/dmcc.1990.555429

Cited by 9 publications

(9 citation statements)

References 8 publications

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“…The kinematic model [12,13] derives this same equation purely from continuum considerations, and it leads to Gaussian velocity profiles and a parabolic region of flow, which is in reasonable agreement with experimental measurements [14,15,16]. More recently, similar ideas have been employed in cellular automata models [17,18,19]. However, all of these models have a fundamental problem when estimating mixing, that whenever a particle moves from one lattice site to another, it necessarily loses contact with many of its neighbors, violating the slow cagebreaking seen in experiment.…”

Section: Introductionmentioning

confidence: 51%

Fast spot-based multiscale simulations of granular drainage

2010

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We develop a multiscale simulation method for dense granular drainage, based on the recently proposed spot model, where the particle packing flows by local collective displacements in response to diffusing "spots" of interstitial free volume. By comparing with discrete-element method (DEM) simulations of 55,000 spheres in a rectangular silo, we show that the spot simulation is able to approximately capture many features of drainage, such as packing statistics, particle mixing, and flow profiles. The spot simulation runs two to three orders of magnitude faster than DEM, making it an appropriate method for real-time control or optimization. We demonstrate extensions for modeling particle heaping and avalanching at the free surface, and for simulating the boundary layers of slower flow near walls. We show that the spot simulations are robust and flexible, by demonstrating that they can be used in both event-driven and fixed timestep approaches, and showing that the elastic relaxation step used in the model can be applied much less frequently and still create good results.

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Section: Introductionmentioning

confidence: 51%

Fast spot-based multiscale simulations of granular drainage

2010

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“…Powder Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / p ow t e c particular avalanches, segregation, flow [9][10][11][12][13][14] and rearrangements on the surface of three dimensional system due to inertial effects [15]. Sedimentation, soil erosion and debris flow in rivers has also been modeled by cellular automata [16,17].…”

Section: Contents Lists Available At Sciencedirectmentioning

confidence: 98%

Compacity influence in reorganization of two dimensional granular packings: Numerical model

Aguirre

Calvo

2010

Powder Technology

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“…Cellular automata are widely used in the granular mechanics community, because they can represent the essential physics of granular materials at a reasonably low computational cost. Because the principles are often similar to those of lattice-gas automata in fluid dynamics (e.g., Chen and Doolen, 1998), cellular automata for granular mechanics are sometimes referred to as lattice grain models (LGrMs) (Gutt and Haff, 1990;Peng and Herrmann, 1994;Alonso and Herrmann, 1996;Kertész, 1999, 1998;Martinez and Masson, 1998;Désérable, 2002;Cottenceau and Désérable, 2010;Désérable et al, 2011).…”

Section: Model Descriptionmentioning

confidence: 99%

author response to reviewer comments

Tucker¹

2018

Preprint

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This paper describes and explores a new continuous-time stochastic cellular automaton model of hillslope evolution. The Grain Hill model provides a computational framework with which to study slope forms that arise from stochastic disturbance and rock weathering events. The model operates on a hexagonal lattice, with cell states representing fluid, rock, and grain aggregates that are either stationary or in a state of motion in one of the six cardinal lattice directions. Cells representing near-surface soil material undergo stochastic disturbance events, in which initially stationary material is put into motion. Net downslope transport emerges from the greater likelihood for disturbed material to move downhill than to move uphill. Cells representing rock undergo stochastic weathering events in which the rock is converted into regolith. The model can reproduce a range of common slope forms, from fully soil mantled to rocky or partially mantled, and from convex-upward to planar shapes. An optional additional state represents large blocks that cannot be displaced upward by disturbance events. With the addition of this state, the model captures the morphology of hogbacks, scarps, and similar features. In its simplest form, the model has only three process parameters, which represent disturbance frequency, characteristic disturbance depth, and base-level lowering rate, respectively. Incorporating physical weathering of rock adds one additional parameter, representing the characteristic rock weathering rate. These parameters are not arbitrary but rather have a direct link with corresponding parameters in continuum theory. Comparison between observed and modeled slope forms demonstrates that the model can reproduce both the shape and scale of real hillslope profiles. Model experiments highlight the importance of regolith cover fraction in governing both the downslope mass transport rate and the rate of physical weathering. Equilibrium rocky hillslope profiles are possible even when the rate of base-level lowering exceeds the nominal bare-rock weathering rate, because increases in both slope gradient and roughness can allow for rock weathering rates that are greater than the flat-surface maximum. Examples of transient relaxation of steep, rocky slopes predict the formation of a regolith-mantled pediment that migrates headward through time while maintaining a sharp slope break.

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An Automata Model of Granular Materials

Cited by 9 publications

References 8 publications

Fast spot-based multiscale simulations of granular drainage

Fast spot-based multiscale simulations of granular drainage

Compacity influence in reorganization of two dimensional granular packings: Numerical model

author response to reviewer comments

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