93 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
Numerical simulations of granular media composed with irregular polyhedral particles: effect of particles’ angularity
We use contact dynamic simulations to perform a systematic investigation of the effects of particles shape angularity on mechanicals response in sheared granular materials. The particles are irregular polyhedra with varying numbers of face from spheres to “double pyramid” shape with a constant aspect ratio. We study the quasi-static behavior, structural and force anisotropies of several packings subjected to triaxial compression.
An interesting finding is that the shear strength first increases with angularity up to a maximum value and then saturates as the particles become more angular. Analyzing the anisotropies induced by the angular distributions of contacts and forces orientations, we show that the saturation of the shear strength at higher angularities is a consequence of fall-off of the texture anisotropies compensated by an increase of the tangential force
anisotropy. This is attributed to the fact that at higher angularity, particles are better connected (or surrounded) leading to an increase of friction mobilization in order to achieve the deformation. Moreover, the most angular particles also have very few sides so that, this effect is enhanced by the increase of the proportion of face-side and side-side contacts with angularity
Short-time dynamics of a packing of polyhedral grains under horizontal vibrations
We analyze the dynamics of a 3D granular packing composed of particles of
irregular polyhedral shape confined inside a rectangular box with a retaining
wall sub jected to horizontal harmonic forcing. The simulations are performed
by means of the contact dynamics method for a broad set of loading parameters.
We explore the vibrational dynamics of the packing, the evolution of solid
fraction and the scaling of dy- namics with the loading parameters. We show
that the motion of the retaining wall is strongly anharmonic as a result of
jamming and grain rearrangements. It is found that the mean particle
displacement scales with inverse square of frequency, the inverse of the force
amplitude and the square of gravity. The short- time compaction rate grows in
proportion to frequency up to a characteristic frequency, corresponding to
collective particle rearrangements between equilibrium states, and then it
declines in inverse proportion to frequency
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
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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