39 research outputs found
The growth of a Super Stable Heap : an experimental and numerical study
We report experimental and numerical results on the growth of a super stable
heap (SSH). Such a regime appears for flows in a thin channel and for high flow
rate : the flow occurs atop a nearly static heap whose angle is stabilized by
the flowing layer at its top and the side wall friction. The growth of the
static heap is investigated in this paper. A theoretical analysis inspired by
the BRCE formalism predicts the evolution of the growth process, which is
confirmed by both experiments and numerical simulations. The model allows us to
link the characteristic time of the growth to the exchange rate between the
"moving" and "static" grains. We show that this rate is proportional to the
height of the flowing layer even for thick flows. The study of upstream
traveling waves sheds new light on the BCRE model
New patterns in high-speed granular flows
We report on new patterns in high-speed flows of granular materials obtained
by means of extensive numerical simulations. These patterns emerge from the
destabilization of unidirectional flows upon increase of mass holdup and
inclination angle, and are characterized by complex internal structures
including secondary flows, heterogeneous particle volume fraction, symmetry
breaking and dynamically maintained order. In particular, we evidenced steady
and fully developed "supported" flows, which consist of a dense core surrounded
by a highly energetic granular gas. Interestingly, despite their overall
diversity, these regimes are shown to obey a scaling law for the mass flow rate
as a function of the mass holdup. This unique set of 3D flow regimes raises new
challenges for extending the scope of current granular rheological models
Shallow granular flows down flat frictional channels: steady flows and longitudinal vortices
Granular flows down inclined channels with smooth boundaries are common in
nature and in the industry. Nevertheless, the common setup of flat boundaries
has comparatively been much less investigated than the bumpy boundaries one,
which is used by most experimental and numerical studies to avoid sliding
effects. Using DEM numerical simulations with side walls we recover
quantitatively experimental results. At larger angles we predict a rich
behavior, including granular convection and inverted density profiles
suggesting a Rayleigh-B\'enard type of instability. In many aspects flows on a
flat base can be seen as flows over an effective bumpy base made of the basal
rolling layer, giving Bagnold-type profiles in the overburden over that layer.
We have tested a simple viscoplastic rheological model (Nature 2006, vol 441,
pp727-730) in average form. The transition between the unidirectional and the
convective flows is then clearly apparent as a discontinuity in the
constitutive relation.Comment: Minor revision with updated figure
Representation of Functional Data in Neural Networks
Functional Data Analysis (FDA) is an extension of traditional data analysis
to functional data, for example spectra, temporal series, spatio-temporal
images, gesture recognition data, etc. Functional data are rarely known in
practice; usually a regular or irregular sampling is known. For this reason,
some processing is needed in order to benefit from the smooth character of
functional data in the analysis methods. This paper shows how to extend the
Radial-Basis Function Networks (RBFN) and Multi-Layer Perceptron (MLP) models
to functional data inputs, in particular when the latter are known through
lists of input-output pairs. Various possibilities for functional processing
are discussed, including the projection on smooth bases, Functional Principal
Component Analysis, functional centering and reduction, and the use of
differential operators. It is shown how to incorporate these functional
processing into the RBFN and MLP models. The functional approach is illustrated
on a benchmark of spectrometric data analysis.Comment: Also available online from:
http://www.sciencedirect.com/science/journal/0925231
Experimental compaction of anisotropic granular media
We report on experiments to measure the temporal and spatial evolution of
packing arrangements of anisotropic and weakly confined granular material,
using high-resolution -ray adsorption. In these experiments, the
particle configurations start from an initially disordered,
low-packing-fraction state and under vertical solicitations evolve to a dense
state. We find that the packing fraction evolution is slowed by the grain
anisotropy but, as for spherically shaped grains, can be well fitted by a
stretched exponential. For a given type of grains, the characteristic times of
relaxation and of convection are found to be of the same order of magnitude. On
the contrary compaction mechanisms in the media strongly depend on the grain
anisotropy.Comment: to appear in the european physical journal E (EPJE
Aspects of probabilistic modelling for data analysis
Computer technologies have revolutionised the processing of information and the search for knowledge. With the ever increasing computational power, it is becoming possible to tackle new data analysis applications as diverse as mining the Internet resources, analysing drugs effects on the organism or assisting wardens with autonomous video detection techniques.
Fundamentally, the principle of any data analysis task is to fit a model which encodes well the dependencies (or patterns) present in the data. However, the difficulty is precisely to define such proper model when data are noisy, dependencies are highly stochastic and there is no simple physical rule to represent them.
The aim of this work is to discuss the principles, the advantages and weaknesses of the probabilistic modelling framework for data analysis. The main idea of the framework is to model dispersion of data as well as uncertainty about the model itself by probability distributions. Three data analysis tasks are presented and for each of them the discussion is based on experimental results from real datasets.
The first task considers the problem of linear subspaces identification. We show how one can replace a Gaussian noise model by a Student-t noise to make the identification more robust to atypical samples and still keep the learning procedure simple. The second task is about regression applied more specifically to near-infrared spectroscopy datasets. We show how spectra should be pre-processed before entering the regression model. We then analyse the validity of the Bayesian model selection principle for this application (and in particular within the Gaussian Process formulation) and compare this principle to the resampling selection scheme. The final task considered is Collaborative Filtering which is related to applications such as recommendation for e-commerce and text mining. This task is illustrative of the way how intuitive considerations can guide the design of the model and the choice of the probability distributions appearing in it. We compare the intuitive approach with a simpler matrix factorisation approach.(FSA 3)--UCL, 200
Collaborative filtering with interlaced generalized linear models
Collaborative filtering (CF) is a data analysis task appearing in many challenging applications, in particular data mining in Internet and e-commerce. CF can often be formulated as identifying patterns in a large and mostly empty rating matrix. In this paper, we focus on predicting unobserved ratings. This task is often a part of a recommendation procedure. We propose a new CF approach called interlaced generalized linear models (GLM); it is based on a factorization of the rating matrix and uses probabilistic modeling to represent uncertainty in the ratings. The advantage of this approach is that different configurations, encoding different intuitions about the rating process can easily be tested while keeping the same learning procedure. The GLM formulation is the keystone to derive an efficient learning procedure, applicable to large datasets. We illustrate the technique on three public domain datasets. r 2008 Elsevier B.V. All rights reserved
Leidenfrost Granular Flows
International audienceThis paper presents numerical findings on rapid 2D and 3D granular flows on a bumpy base. In the supported regime studied here, a strongly sheared, dilute and agitated layer spontaneously appears at the base of the flow and supports a compact packing of grains moving as a whole. In this regime, the flow behaves like a sliding block on the bumpy base. In particular, for flows on a horizontal base, the average velocity decreases linearly in time and the average kinetic energy decreases linearly with the travelled distance, those features being characteristic of solid-like friction. This allows us to define and measure an effective friction coefficient, which is independent of the mass and velocity of the flow. This coefficient only loosely depends on the value of the micromechanical friction coefficient whereas the influence of the bumpiness of the base is strong. We give evidence that this dilute and agitated layer does not result in significantly less friction. Finally, we show that a steady regime of supported flows can exist on inclines whose angle is carefully chosen