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A cylindrical cavity in a noncohesive granular medium will collapse under gravity, leaving a circular crater in the surface of the material. We study this process through experiment and numerical modeling. Experimentally, we deter...
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A cylindrical cavity in a noncohesive granular medium will collapse under gravity, leaving a circular crater in the surface of the material. We study this process through experiment and numerical modeling. Experimentally, we determine the shape and dimensions of craters formed by the collapse of a cylindrical cavity in a bed of small glass beads. Using a depth-averaged continuum model with cylindrical symmetry, we calculate the shape of the free surface both during and after the collapse. We use the model to study the energetics of the collapse process and investigate the dependence of the final crater on the initial shape of the cavity and the initial velocity field. While the shapes of the final craters are not identical in model and experiment, we find good qualitative agreement in aspect ratio and slope.
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In spite of the evident diversity of models of signals and time series, there is still an urgent need to develop constructs that are both accurate and highly interpretable (human-centric). While a great deal of research has been d...
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In spite of the evident diversity of models of signals and time series, there is still an urgent need to develop constructs that are both accurate and highly interpretable (human-centric). While a great deal of research has been devoted to the design of nonlinear models of time series (with anticipation of achieving high accuracy of prediction), an issue of interpretability (transparency) of the models remains an evident and ongoing challenge. The user-friendliness of models of time series comes hand in hand with an ability of humans to perceive and process abstract entities rather than plain numeric entities. With this regard, information granules and Granular Computing play an essential role. The use of information granules gives rise to a concept of granular models of time series or granular models of signals and time series, in brief. A granular interpretation of temporal data, where the role of information granularity is of paramount interest and effectively supports a human-centric description of relationships existing within data. This study revisits generic concepts of information granules and Granular Computing in this setting and elaborates on a fundamental way of forming information granules (both sets - intervals as well as fuzzy sets) through applying a principle of justifiable granularity. The granular representation of time series is then discussed with a number of representation alternatives. A question of forming adjustable temporal slices (time windows) using which information granules are formed is discussed. With this regard presented is an optimization criterion of a sum of volumes of information granules whose minimization is realized through some methods of evolutionary or populationbased optimization techniques. A series of illustrative examples is also discussed.
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摘要 :AbstractThe measurement of granules is often considered the most foundational problem in granular computing and it has been studied in many fields but in relative isolation. This paper attempts to explore the measurement for gener...
展开AbstractThe measurement of granules is often considered the most foundational problem in granular computing and it has been studied in many fields but in relative isolation. This paper attempts to explore the measurement for general granules, whether they are granules based on equivalence or general relations, whether they are macrocosmic or microcosmic granules, and whether they are granules on a finite or an infinite set. For a finite set we discuss the measurement of granules corresponding to equivalence relations and introduce definitions of granularity, fineness and granular entropy. In order to distinguish those granules with the same granularity, fineness and granular entropy we present conditional granularity, conditional fineness and conditional granular entropy and obtain the necessary and sufficient condition which can judge one granule as coarser or finer than another. While the conditional granularity is a subsethood measure which satisfies monotonic properties. What’s more, we introduce relation matrix to measure the granules, and it not only can be easily generalized to measure the granules on general relations but also connects granular computing to graph theory. For an infinite set we can define different granularities in different questions, but we suggest the basic idea of granularity, that is, the granularity of a granule is the sum of the relative information contents of its atomic granules.]]>
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Flowing granular materials segregate due to differences in particle size (driven by percolation) and density (driven by buoyancy). Modelling the segregation of mixtures of large/heavy particles and small/light particles is challen...
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Flowing granular materials segregate due to differences in particle size (driven by percolation) and density (driven by buoyancy). Modelling the segregation of mixtures of large/heavy particles and small/light particles is challenging due to the opposing effects of the two segregation mechanisms. Using discrete element method (DEM) simulations of combined size and density segregation we show that the segregation velocity is well described by a model that depends linearly on the local shear rate and quadratically on the species concentration for free surface flows. Concentration profiles predicted by incorporating this segregation velocity model into a continuum advection-diffusion-segregation transport model match DEM simulation results well for a wide range of particle size and density ratios. Most surprisingly, the DEM simulations and the segregation velocity model both show that the segregation direction for a range of size and density ratios depends on the local species concentration. This leads to a methodology to determine the combination of particle size ratio, density ratio and particle concentration for which a bidisperse mixture will not segregate.
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In the past ten years much work has been undertaken on developing mixture theory continuum models to describe kinetic sieving-driven size segregation. We propose an extension to these models that allows their application to bidisp...
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In the past ten years much work has been undertaken on developing mixture theory continuum models to describe kinetic sieving-driven size segregation. We propose an extension to these models that allows their application to bidisperse flows over inclined channels, with particles varying in density and size. Our model incorporates both a recently proposed explicit formula for how the total pressure is distributed among different species of particles, which is one of the key elements of mixture theory-based kinetic sieving models, and a shear rate-dependent drag. The resulting model is used to predict the range of particle sizes and densities for which the mixture segregates. The prediction of no segregation in the model is benchmarked by using discrete particle simulations, and good agreement is found when a single fitting parameter is used which determines whether the pressure scales with the diameter, surface area or volume of the particle.
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We develop a theoretical description for mechanically stable frictional packings in terms of the difference between the total number of contacts required for isostatic packings of frictionless disks and the number of contacts in f...
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We develop a theoretical description for mechanically stable frictional packings in terms of the difference between the total number of contacts required for isostatic packings of frictionless disks and the number of contacts in frictional packings, m = N_c~0 - N_c. The saddle order m represents the number of unconstrained degrees of freedom that a static packing would possess if friction were removed. Using a novel numerical method that allows us to enumerate disk packings for each m, we show that the probability to obtain a packing with saddle order m at a given static friction coefficient μ, P_m(μ), can be expressed as a power series in μ. Using this form for P_m(μ), we quantitatively describe the dependence of the average contact number on the friction coefficient for static disk packings obtained from direct simulations of the Cundall-Strack model for all μ and N.
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We present measurements of the stress as a function of vertical position in a column of granular material sheared in a cylindrical Couette device. All three components of the stress tensor on the outer cylinder were measured as a ...
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We present measurements of the stress as a function of vertical position in a column of granular material sheared in a cylindrical Couette device. All three components of the stress tensor on the outer cylinder were measured as a function of distance from the free surface at shear rates low enough that the material was in the dense, slow flow regime. We find that the stress profile differs fundamentally from that of fluids, from the predictions of plasticity theories, and from intuitive expectation. We argue that the anomalous stress profile is due to an anisotropic fabric caused by the combined action of gravity and shear.
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In order to better understand the mechanism governing segregation in dense granular flows, the force experienced by a large particle embedded in a granular flow made of small particles is studied using discrete numerical simulatio...
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In order to better understand the mechanism governing segregation in dense granular flows, the force experienced by a large particle embedded in a granular flow made of small particles is studied using discrete numerical simulations. Accurate force measurements have been obtained in a large range of flow parameters by trapping the large particle in a harmonic potential well to mimic an optical tweezer. Results show that positive or negative segregation lift forces (perpendicular to the shear) exist depending on the stress inhomogeneity. An empirical expression of the segregation force is proposed as a sum of a term proportional to the gradient of pressure and a term proportional to the gradient of shear stress, which both depend on the local friction and particle size ratio.
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One can granulate data and information in multiple ways to generate granulation hierarchies. What the characteristics of such hierarchies are and what consequences they have on levels of granularity is, however, left implicit. We ...
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One can granulate data and information in multiple ways to generate granulation hierarchies. What the characteristics of such hierarchies are and what consequences they have on levels of granularity is, however, left implicit. We propose an explicit representation of such additional information of granulation hierarchies and transform them to granular perspectives. Granular perspectives can be uniquely identified, hence, distinguished, by means of formally representing their semantics using a granulation criterion and type of granularity used for granulation. The granular perspectives are equipped with both a simple relation and with mereological relations to consistently relate them, thereby facilitating cross-granular querying. Given the premises, definitions, and proven properties, consequences for characterising levels of granularity within such perspectives are demonstrated.
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The response of a granular material during a stop-and-go shear experiment is investigated using an annular shear cell and silicagel powers of different particle sizes. The experimental results are examined on the basis of the Diet...
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The response of a granular material during a stop-and-go shear experiment is investigated using an annular shear cell and silicagel powers of different particle sizes. The experimental results are examined on the basis of the Dieterich-Rice-Ruina model for solid friction. In addition to making this analogy with solid friction, we describe a new instability that is observed when restarting shear, where the powder bed is found to slip and compact for short hold times but only dilates for long hold times. The minimum hold time to restore a non-slip behaviour has been investigated for different size particles and normal loadings. The observed dependencies show analogies between this behaviour and the sliding rearrangements seen above the stick-slip threshold.
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