143 research outputs found
Force chains and contact network topology in packings of elongated particles
By means of contact dynamic simulations, we investigate the contact network
topology and force chains in two-dimensional packings of elongated particles
modeled by rounded-cap rectangles. The morphology of large packings of
elongated particles in quasistatic equilibrium is complex due to the combined
effects of local nematic ordering of the particles and orientations of contacts
between particles. We show that particle elongation affects force distributions
and force/fabric anisotropy via various local structures allowed by steric
exclusions and the requirement of force balance. As a result, the force
distributions become increasingly broader as particles become more elongated.
Interestingly, the weak force network transforms from a passive stabilizing
agent with respect to strong force chains to an active force-transmitting
network for the whole system. The strongest force chains are carried by
side/side contacts oriented along the principal stress direction.Comment: Soumis a Physical Review
Multiplicative decompositions and frequency of vanishing of nonnegative submartingales
In this paper, we establish a multiplicative decomposition formula for
nonnegative local martingales and use it to characterize the set of continuous
local submartingales Y of the form Y=N+A, where the measure dA is carried by
the set of zeros of Y. In particular, we shall see that in the set of all local
submartingales with the same martingale part in the multiplicative
decomposition, these submartingales are the smallest ones. We also study some
integrability questions in the multiplicative decomposition and interpret the
notion of saturated sets in the light of our results.Comment: Typos corrected. Close to the published versio
Impact of grading on steady-state strength
International audienceIn the mining industry, waste dumps are earthen structures typically built by loose waste tipping. They may reach heights of hundreds of metres and undergo large deformations. For this reason, their stability design is based on the steady-state shear strength of the waste material. Waste materials are widely graded and may contain particles of up to metric order. Particle shape depends on the pattern of dissecting discontinuities at the source rock mass and the relation between the size of the fragments and discontinuity spacing. The shear strength of this material is determined in the laboratory using scaled samples with altered particle-size distribution (PSD). However, altering the PSD is known to impact shear strength, and this impact is poorly studied. The representativeness of laboratory parameters obtained from scaled samples is thus arguable. Discrete-element simulations are used here to investigate steady-state shear strength changes with the alteration of the PSD when particle size and shape are correlated. It is observed that shear strength changes result from the variation of the particle shapes induced by the alteration of the PSD. Consequently, identifying size−shape correlations and their potential impact on shear strength is of paramount importance when scaling materials for laboratory testing
Stress-strain behavior and geometrical properties of packings of elongated particles
We present a numerical analysis of the effect of particle elongation on the
quasistatic behavior of sheared granular media by means of the Contact Dynamics
method. The particle shapes are rounded-cap rectangles characterized by their
elongation. The macroscopic and microstructural properties of several packings
subjected to biaxial compression are analyzed as a function of particle
elongation. We find that the shear strength is an increasing linear function of
elongation. Performing an additive decomposition of the stress tensor based on
a harmonic approximation of the angular dependence of branch vectors, contact
normals and forces, we show that the increasing mobilization of friction force
and the associated anisotropy are key effects of particle elongation. These
effects are correlated with partial nematic ordering of the particles which
tend to be oriented perpendicular to the major principal stress direction and
form side-to-side contacts. However, the force transmission is found to be
mainly guided by cap-to-side contacts, which represent the largest fraction of
contacts for the most elongated particles. Another interesting finding is that,
in contrast to shear strength, the solid fraction first increases with particle
elongation, but declines as the particles become more elongated. It is also
remarkable that the coordination number does not follow this trend so that the
packings of more elongated particles are looser but more strongly connected.Comment: Submited to Physical Review
Vibrational dynamics of confined granular material
By means of two-dimensional contact dynamics simulations, we analyze the
vibrational dynamics of a confined granular layer in response to harmonic
forcing. We use irregular polygonal grains allowing for strong variability of
solid fraction. The system involves a jammed state separating passive (loading)
and active (unloading) states. We show that an approximate expression of the
packing resistance force as a function of the displacement of the free
retaining wall from the jamming position provides a good description of the
dynamics. We study in detail the scaling of displacements and velocities with
loading parameters. In particular, we find that, for a wide range of
frequencies, the data collapse by scaling the displacements with the inverse
square of frequency, the inverse of the force amplitude and the square of
gravity. Interestingly, compaction occurs during the extension of the packing,
followed by decompaction in the contraction phase. We show that the mean
compaction rate increases linearly with frequency up to a characteristic
frequency and then it declines in inverse proportion to frequency. The
characteristic frequency is interpreted in terms of the time required for the
relaxation of the packing through collective grain rearrangements between two
equilibrium states
Force transmission in a packing of pentagonal particles
We perform a detailed analysis of the contact force network in a dense
confined packing of pentagonal particles simulated by means of the contact
dynamics method. The effect of particle shape is evidenced by comparing the
data from pentagon packing and from a packing with identical characteristics
except for the circular shape of the particles. A counterintuitive finding of
this work is that, under steady shearing, the pentagon packing develops a lower
structural anisotropy than the disk packing. We show that this weakness is
compensated by a higher force anisotropy, leading to enhanced shear strength of
the pentagon packing. We revisit "strong" and "weak" force networks in the
pentagon packing, but our simulation data provide also evidence for a large
class of "very weak" forces carried mainly by vertex-to-edge contacts. The
strong force chains are mostly composed of edge-to-edge contacts with a marked
zig-zag aspect and a decreasing exponential probability distribution as in a
disk packing
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Scaling Behavior of Cohesive Self-Gravitating Aggregates
By means of extensive three-dimensional contact dynamics simulations, we analyze the strength properties and microstructure of a granular asteroid, modeled as a self-gravitating cohesive granular aggregate composed of spherical particles, and subjected to diametrical compression tests. We show that, for a broad range of system parameters (shear rate, cohesive forces, asteroid diameter), the behavior can be described by a modified inertial number that incorporates interparticle cohesion and gravitational forces. At low inertial numbers, the behavior is ductile with a well-defined stress peak that scales with internal pressure with a prefactor 0.9. As the inertial number increases, both the prefactor and fluctuations around the mean increase, evidencing a dynamical crisis resulting from the destabilizing effect of particle inertia. From a micromechanical description of the contact and force networks, we propose a model that accounts for solid fraction, local stress, particle connectivity, and granular texture. In the limit of small inertial numbers, we find a very good agreement of the theoretical estimate of compressive strength, evidencing the major role of these structural parameters for the modeled aggregates.</p
Robust pricing and hedging of double no-touch options
Double no-touch options, contracts which pay out a fixed amount provided an
underlying asset remains within a given interval, are commonly traded,
particularly in FX markets. In this work, we establish model-free bounds on the
price of these options based on the prices of more liquidly traded options
(call and digital call options). Key steps are the construction of super- and
sub-hedging strategies to establish the bounds, and the use of Skorokhod
embedding techniques to show the bounds are the best possible.
In addition to establishing rigorous bounds, we consider carefully what is
meant by arbitrage in settings where there is no {\it a priori} known
probability measure. We discuss two natural extensions of the notion of
arbitrage, weak arbitrage and weak free lunch with vanishing risk, which are
needed to establish equivalence between the lack of arbitrage and the existence
of a market model.Comment: 32 pages, 5 figure
Particle shape dependence in 2D granular media
Particle shape is a key to the space-filling and strength properties of
granular matter. We consider a shape parameter describing the degree of
distortion from a perfectly spherical shape. Encompassing most specific shape
characteristics such as elongation, angularity and nonconvexity, is a
low-order but generic parameter that we used in a numerical benchmark test for
a systematic investigation of shape-dependence in sheared granular packings
composed of particles of different shapes. We find that the shear strength is
an increasing function of with nearly the same trend for all shapes, the
differences appearing thus to be of second order compared to . We also
observe a nontrivial behavior of packing fraction which, for all our simulated
shapes, increases with from the random close packing fraction for disks,
reaches a peak considerably higher than that for disks, and subsequently
declines as is further increased. These findings suggest that a
low-order description of particle shape accounts for the principal trends of
packing fraction and shear strength. Hence, the effect of second-order shape
parameters may be investigated by considering different shapes at the same
level of .Comment: 5 pages, 8 figure
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