8,811 research outputs found
Metastability of a granular surface in a spinning bucket
The surface shape of a spinning bucket of granular material is studied using
a continuum model of surface flow developed by Bouchaud et al. and Mehta et al.
An experimentally observed central subcritical region is reproduced by the
model. The subcritical region occurs when a metastable surface becomes unstable
via a nonlinear instability mechanism. The nonlinear instability mechanism
destabilizes the surface in large systems while a linear instability mechanism
is relevant for smaller systems. The range of angles in which the granular
surface is metastable vanishes with increasing system size.Comment: 8 pages with postscript figures, RevTex, to appear in Phys. Rev.
Thermal convection in mono-disperse and bi-disperse granular gases: A simulation study
We present results of a simulation study of inelastic hard-disks vibrated in
a vertical container. An Event-Driven Molecular Dynamics method is developed
for studying the onset of convection. Varying the relevant parameters
(inelasticity, number of layers at rest, intensity of the gravity) we are able
to obtain a qualitative agreement of our results with recent hydrodynamical
predictions. Increasing the inelasticity, a first continuous transition from
the absence of convection to one convective roll is observed, followed by a
discontinuous transition to two convective rolls, with hysteretic behavior. At
fixed inelasticity and increasing gravity, a transition from no convection to
one roll can be evidenced. If the gravity is further increased, the roll is
eventually suppressed. Increasing the number of monolayers the system
eventually localizes mostly at the bottom of the box: in this case multiple
convective rolls as well as surface waves appear. We analyze the density and
temperature fields and study the existence of symmetry breaking in these fields
in the direction perpendicular to the injection of energy. We also study a
binary mixture of grains with different properties (inelasticity or diameters).
The effect of changing the properties of one of the components is analyzed,
together with density, temperature and temperature ratio fields.
Finally, the presence of a low-fraction of quasi-elastic impurities is shown
to determine a sharp transition between convective and non-convective steady
states.Comment: 11 pages, 12 figures, accepted for publication on Physical Review
Efficient Cross-Validation of Echo State Networks
Echo State Networks (ESNs) are known for their fast and precise one-shot
learning of time series. But they often need good hyper-parameter tuning for
best performance. For this good validation is key, but usually, a single
validation split is used. In this rather practical contribution we suggest
several schemes for cross-validating ESNs and introduce an efficient algorithm
for implementing them. The component that dominates the time complexity of the
already quite fast ESN training remains constant (does not scale up with )
in our proposed method of doing -fold cross-validation. The component that
does scale linearly with starts dominating only in some not very common
situations. Thus in many situations -fold cross-validation of ESNs can be
done for virtually the same time complexity as a simple single split
validation. Space complexity can also remain the same. We also discuss when the
proposed validation schemes for ESNs could be beneficial and empirically
investigate them on several different real-world datasets.Comment: Accepted in ICANN'19 Workshop on Reservoir Computin
A Model for Force Fluctuations in Bead Packs
We study theoretically the complex network of forces that is responsible for
the static structure and properties of granular materials. We present detailed
calculations for a model in which the fluctuations in the force distribution
arise because of variations in the contact angles and the constraints imposed
by the force balance on each bead of the pile. We compare our results for force
distribution function for this model, including exact results for certain
contact angle probability distributions, with numerical simulations of force
distributions in random sphere packings. This model reproduces many aspects of
the force distribution observed both in experiment and in numerical simulations
of sphere packings
Optoelectronic Reservoir Computing
Reservoir computing is a recently introduced, highly efficient bio-inspired
approach for processing time dependent data. The basic scheme of reservoir
computing consists of a non linear recurrent dynamical system coupled to a
single input layer and a single output layer. Within these constraints many
implementations are possible. Here we report an opto-electronic implementation
of reservoir computing based on a recently proposed architecture consisting of
a single non linear node and a delay line. Our implementation is sufficiently
fast for real time information processing. We illustrate its performance on
tasks of practical importance such as nonlinear channel equalization and speech
recognition, and obtain results comparable to state of the art digital
implementations.Comment: Contains main paper and two Supplementary Material
Hierarchical Temporal Representation in Linear Reservoir Computing
Recently, studies on deep Reservoir Computing (RC) highlighted the role of
layering in deep recurrent neural networks (RNNs). In this paper, the use of
linear recurrent units allows us to bring more evidence on the intrinsic
hierarchical temporal representation in deep RNNs through frequency analysis
applied to the state signals. The potentiality of our approach is assessed on
the class of Multiple Superimposed Oscillator tasks. Furthermore, our
investigation provides useful insights to open a discussion on the main aspects
that characterize the deep learning framework in the temporal domain.Comment: This is a pre-print of the paper submitted to the 27th Italian
Workshop on Neural Networks, WIRN 201
Clustering and Non-Gaussian Behavior in Granular Matter
We investigate the properties of a model of granular matter consisting of
Brownian particles on a line subject to inelastic mutual collisions. This model
displays a genuine thermodynamic limit for the mean values of the energy and
the energy dissipation. When the typical relaxation time associated with
the Brownian process is small compared with the mean collision time
the spatial density is nearly homogeneous and the velocity probability
distribution is gaussian. In the opposite limit one has
strong spatial clustering, with a fractal distribution of particles, and the
velocity probability distribution strongly deviates from the gaussian one.Comment: 4 pages including 3 eps figures, LaTex, added references, corrected
typos, minimally changed contents and abstract, to published in
Phys.Rev.Lett. (tentatively on 28th of October, 1998
Volume fluctuations and geometrical constraints in granular packs
Structural organization and correlations are studied in very large packings
of equally sized acrylic spheres, reconstructed in three-dimensions by means of
X-ray computed tomography. A novel technique, devised to analyze correlations
among more than two spheres, shows that the structural organization can be
conveniently studied in terms of a space-filling packing of irregular
tetrahedra. The study of the volume distribution of such tetrahedra reveals an
exponential decay in the region of large volumes; a behavior that is in very
good quantitative agreement with theoretical prediction. I argue that the
system's structure can be described as constituted of two phases: 1) an
`unconstrained' phase which freely shares the volume; 2) a `constrained' phase
which assumes configurations accordingly with the geometrical constraints
imposed by the condition of non-overlapping between spheres and mechanical
stability. The granular system exploits heterogeneity maximizing freedom and
entropy while constraining mechanical stability.Comment: 5 pages, 4 figure
Intruders in the Dust: Air-Driven Granular Size Separation
Using MRI and high-speed video we investigate the motion of a large intruder
particle inside a vertically shaken bed of smaller particles. We find a
pronounced, non-monotonic density dependence, with both light and heavy
intruders moving faster than those whose density is approximately that of the
granular bed. For light intruders, we furthermore observe either rising or
sinking behavior, depending on intruder starting height, boundary condition and
interstitial gas pressure. We map out the phase boundary delineating the rising
and sinking regimes. A simple model can account for much of the observed
behavior and show how the two regimes are connected by considering pressure
gradients across the granular bed during a shaking cycle.Comment: 5 pages, 4 figure
Logarithmic Relaxations in a Random Field Lattice Gas Subject to Gravity
A simple lattice gas model with random fields and gravity is introduced to
describe a system of grains moving in a disordered environment. Off equilibrium
relaxations of bulk density and its two time correlation functions are
numerically found to show logarithmic time dependences and "aging" effects.
Similitudes with dry granular media are stressed. The connections with off
equilibrium dynamics in others kinds of "frustrated" lattice models in presence
of a directional driving force (gravity) are discussed to single out the
appearance of universal features in the relaxation process.Comment: 15 pages, latex, 7 figures include
- …