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Flow of variably fluidized granular masses across threedimensional terrain
 J. Geophys. Res
, 2001
"... Abstract. Rock avalanches, debris flows, and related phenomena consist of grainfluid mixtures that move across threedimensional terrain. In all these phenomena the same basic forces govern motion, but differing mixture compositions, initial conditions, and boundary conditions yield varied dynamics ..."
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Cited by 63 (5 self)
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Abstract. Rock avalanches, debris flows, and related phenomena consist of grainfluid mixtures that move across threedimensional terrain. In all these phenomena the same basic forces govern motion, but differing mixture compositions, initial conditions, and boundary conditions yield varied dynamics and deposits. To predict motion of diverse grainfluid masses from initiation to deposition, we develop a depthaveraged, threedimensional mathematical model that accounts explicitly for solid and fluidphase forces and interactions. Model input consists of initial conditions, path topography, basal and internal friction angles of solid grains, viscosity of pore fluid, mixture density, and a mixture diffusivity that controls pore pressure dissipation. Because these properties are constrained by independent measurements, the model requires little or no calibration and yields readily testable predictions. In the limit of vanishing Coulomb friction due to persistent high fluid pressure the model equations describe motion of viscous floods, and in the limit of vanishing fluid stress they describe onephase granular avalanches. Analysis of intermediate phenomena such as debris flows and pyroclastic flows requires use of the full mixture equations, which can simulate interaction of highfriction surge fronts with
Symmetric Monoidal and Cartesian Double Categories as a Semantic Framework for Tile Logic
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2002
"... Tile systems offer a general paradigm for modular descriptions of concurrent systems, based on a set of rewriting rules with sideeffects. Monoidal double categories are a natural semantic framework for tile systems, because the mathematical structures describing system states and synchronizing acti ..."
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Cited by 14 (9 self)
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Tile systems offer a general paradigm for modular descriptions of concurrent systems, based on a set of rewriting rules with sideeffects. Monoidal double categories are a natural semantic framework for tile systems, because the mathematical structures describing system states and synchronizing actions (called configurations and observations, respectively, in our terminology) are monoidal categories having the same objects (the interfaces of the system). In particular, configurations and observations based on netprocesslike and term structures are usually described in terms of symmetric monoidal and cartesian categories, where the auxiliary structures for the rearrangement of interfaces correspond to suitable natural transformations. In this paper we discuss the lifting of these auxiliary structures to double categories. We notice that the internal construction of double categories produces a pathological asymmetric notion of natural transformation, which is fully exploited in one dimension only (for example, for configurations or for observations, but not for both). Following Ehresmann (1963), we overcome this biased definition, introducing the notion of generalized natural transformation between four double functors (rather than two). As a consequence, the concepts of symmetric monoidal and cartesian (with consistently chosen products) double categories arise in a natural way from the corresponding ordinary versions, giving a very good relationship between the auxiliary structures of configurations and observations. Moreover, the Kelly–Mac Lane coherence axioms can be lifted to our setting without effort, thanks to the characterization of two suitable diagonal categories that are always present in a double category. Then, symmetric monoidal and cartesian double categories are shown to offer an adequate semantic setting for process and term tile systems.
Executable Tile Specifications for Process Calculi
, 1999
"... . Tile logic extends rewriting logic by taking into account sideeffects and rewriting synchronization. These aspects are very important when we model process calculi, because they allow us to express the dynamic interaction between processes and "the rest of the world". Since rewriting log ..."
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Cited by 14 (10 self)
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. Tile logic extends rewriting logic by taking into account sideeffects and rewriting synchronization. These aspects are very important when we model process calculi, because they allow us to express the dynamic interaction between processes and "the rest of the world". Since rewriting logic is the semantic basis of several language implementation efforts, an executable specification of tile systems can be obtained by mapping tile logic back into rewriting logic, in a conservative way. However, a correct rewriting implementation of tile logic requires the development of a metalayer to control rewritings, i.e., to discard computations that do not correspond to any deduction in tile logic. We show how such methodology can be applied to term tile systems that cover and extend a wideclass of SOS formats for the specification of process calculi. The wellknown casestudy of full CCS, where the term tile format is needed to deal with recursion (in the form of the replicator operator), is di...
Symmetric and Cartesian Double Categories as a Semantic Framework for Tile Logic
, 1995
"... this paper we discuss the lifting of these auxiliary structures to double categories. We notice that the internal construction of double categories produces a pathological asymmetric notion of natural transformation, which is fully exploited in one dimension only (e.g., for configurations or for eff ..."
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Cited by 6 (5 self)
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this paper we discuss the lifting of these auxiliary structures to double categories. We notice that the internal construction of double categories produces a pathological asymmetric notion of natural transformation, which is fully exploited in one dimension only (e.g., for configurations or for effects, but not for both). Following Ehresmann (1963), we overcome this biased definition, introducing the notion of generalized natural transformation between four
A 2category View for Double Categories with Shared Structure
, 1999
"... 2categories and double categories are respectively the natural semantic ground for rewriting logic (rl) and tile logic (tl). Since 2categories can be regarded as a special case of double categories, then rl can be easily embedded into tl, where also rewriting synchronization is considered. Since ..."
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2categories and double categories are respectively the natural semantic ground for rewriting logic (rl) and tile logic (tl). Since 2categories can be regarded as a special case of double categories, then rl can be easily embedded into tl, where also rewriting synchronization is considered. Since rl is the semantic basis of several existing languages, it is useful to map tl back into rl to have an executable framework for tile specifications. We extend the results of a previous work of two of the authors, focusing on tile systems where the algebraic structures for configurations and observations rely on some common auxiliary structure (e.g., for pairing, projecting, etc.). The new model theory required to relate the categorical models of the two logics is an extended version of the theory of 2categories, and is defined using partial membership equational logic. More concretely, this semantic mapping yields a rewriting logic implementation of tile logic, where a metalayer is requir...
A Logic for Modular Descriptions of Asynchronous and Synchronized Concurrent Systems
, 1998
"... Tile logic is a framework to reason about the dynamic evolution of concurrent systems in a modular way, and it extends rewriting logic (in the unconditional case) by rewriting synchronization and side effects. The subject of this dissertation concerns some interesting tile models of computation such ..."
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Tile logic is a framework to reason about the dynamic evolution of concurrent systems in a modular way, and it extends rewriting logic (in the unconditional case) by rewriting synchronization and side effects. The subject of this dissertation concerns some interesting tile models of computation such that the mathematical structures representing configurations (i.e., system states) and effects (i.e., observable actions) have in common some auxiliary structure (e.g., for tupling, projecting, etc.). In particular, two such logics (called process and term tile logic respectively) are fully discussed, where netprocesslike and usual term structures are employed. The categorical models for the two logics are introduced in terms of suitable classes of double categories. Then, the new model theory of 2EVHcategories is proposed to relate the categorical models of tile logic and rewriting logic. This is particularly important, because rewriting logic is the semantic basis of several language i...
Green’s Function Measurements in 2D Granular Materials
, 2002
"... We describe experiments that probe the response to a point force of 2D granular systems under a variety of conditions. Using photoelastic particles to determine forces at the grain scale, we obtain ensembles of responses for the following particle types, packing geometries and conditions: monodisper ..."
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We describe experiments that probe the response to a point force of 2D granular systems under a variety of conditions. Using photoelastic particles to determine forces at the grain scale, we obtain ensembles of responses for the following particle types, packing geometries and conditions: monodisperse ordered hexagonal packings of disks, bidisperse packings of disks with different amount of disorder, disks packed in a regular rectangular lattice, packings of pentagonal particles, systems with forces applied at an arbitrary angle at the surface, and systems prepared with shear deformation, hence with texture or anisotropy. We experimentally show that disorder, packing structure, friction and texture significantly affect the average force response in granular systems. For packings with weak disorder, the mean forces propagate primarily along lattice directions. The width of the response along these preferred directions grows with depth, increasingly so as the disorder of the system grows. Also, as the disorder increases, the two propagation directions of the mean force merge into a single direction. The response function for the mean force in the most strongly disordered system is quantitatively consistent with an elastic description
Green’s Function Measurements of Force Transmission in 2D Granular Materials
, 2003
"... We describe experiments that probe the response to a point force of 2D granular systems under a variety of conditions. Using photoelastic particles to determine forces at the grain scale, we obtain ensembles of responses for the following particle types, packing geometries and conditions: monodisper ..."
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We describe experiments that probe the response to a point force of 2D granular systems under a variety of conditions. Using photoelastic particles to determine forces at the grain scale, we obtain ensembles of responses for the following particle types, packing geometries and conditions: monodisperse ordered hexagonal packings of disks, bidisperse packings of disks with different amount of disorder, disks packed in a regular rectangular lattice with different frictional properties, packings of pentagonal particles, systems with forces applied at an arbitrary angle at the surface, and systems prepared with shear deformation, hence with texture or anisotropy. We experimentally show that disorder, packing structure, friction and texture significantly affect the average force response in granular systems. For packings with weak disorder, the mean forces propagate primarily along lattice directions. The width of the response along these preferred directions grows with depth, increasingly so as the disorder of the system grows. Also, as the disorder increases, the two propagation directions of the mean force merge into a single direction. The response function for the mean force in the most strongly disordered system is quantitatively consistent with an elastic description for forces applied nearly normally to a surface, but this description is not as good for nonnormal applied forces. These observations are consistent with recent predictions of Bouchaud et al. [Bouchaud et al.,
Slow Drag in 2D Granular Media
, 2008
"... We study the drag force experienced by an object slowly moving at constant velocity through a 2D granular material consisting of bidisperse disks. The drag force is dominated by force chain structures in the bulk of the system, thus showing strong fluctuations. We consider the effect of three import ..."
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We study the drag force experienced by an object slowly moving at constant velocity through a 2D granular material consisting of bidisperse disks. The drag force is dominated by force chain structures in the bulk of the system, thus showing strong fluctuations. We consider the effect of three important control parameters for the system: the packing fraction, the drag velocity and the size of the tracer particle. We find that the mean drag force increases as a powerlaw (exponent of 1.5) in the reduced packing fraction, (γ − γc)/γc, as γ passes through a critical packing fraction, γc. By comparison, the mean drag grows slowly (basically logarithmic) with the drag velocity, showing a weak ratedependence. We also find that the mean drag force depends nonlinearly on the diameter, a of the tracer particle when a is comparable to the surrounding particles ’ size. However, the system nevertheless exhibits strong statistical invariance in the sense that many physical quantities collapse onto a single curve under appropriate scaling: force distributions P(f) collapse with appropriate scaling by the mean force, the power spectra P(ω) collapse when scaled by the drag velocity, and the avalanche size and duration distributions collapse when scaled by the mean avalanche size and duration. We also show that the system can be understood using simple failure models, which repro1 duce many experimental observations. These observations include: a power law variation of the spectrum with frequency characterized by an exponent α = −2, exponential distributions for both the avalanche size and duration, and an exponential falloff at large forces for the force distributions. These experimental data and simulations indicate that fluctuations in the drag force seem to be associated with the force chain formation and breaking in the system. Moreover, our simulations suggest that the logarithmic increase of the mean drag force with rate can be accounted for if slow relaxation of the force chain networks is included.