75 research outputs found
Dynamics of granular avalanches caused by local perturbations
Surface flow of granular material is investigated within a continuum approach
in two dimensions. The dynamics is described by a non-linear coupling between
the two `states' of the granular material: a mobile layer and a static bed.
Following previous studies, we use mass and momentum conservation to derive
St-Venant like equations for the evolution of the thickness R of the mobile
layer and the profile Z of the static bed. This approach allows the rheology in
the flowing layer to be specified independently, and we consider in details the
two following models: a constant plug flow and a linear velocity profile. We
study and compare these models for non-stationary avalanches triggered by a
localized amount of mobile grains on a static bed of constant slope. We solve
analytically the non-linear dynamical equations by the method of
characteristics. This enables us to investigate the temporal evolution of the
avalanche size, amplitude and shape as a function of model parameters and
initial conditions. In particular, we can compute their large time behavior as
well as the condition for the formation of shocks.Comment: 25 pages, 12 figure
Granular Flows in a Rotating Drum: the Scaling Law between Velocity and Thickness of the Flow
The flow of dry granular material in a half-filled rotating drum is studied.
The thickness of the flowing zone is measured for several rotation speeds, drum
sizes and beads sizes (size ratio between drum and beads ranging from 47 to
7400). Varying the rotation speed, a scaling law linking mean velocity vs
thickness of the flow, , is deduced for each couple (beads, drum).
The obtained exponent is not always equal to 1, value previously reported
in a drum, but varies with the geometry of the system. For small size ratios,
exponents higher than 1 are obtained due to a saturation of the flowing zone
thickness. The exponent of the power law decreases with the size ratio, leading
to exponents lower than 1 for high size ratios. These exponents imply that the
velocity gradient of a dry granular flow in a rotating drum is not constant.
More fundamentally, these results show that the flow of a granular material in
a rotating drum is very sensible to the geometry, and that the deduction of the
``rheology'' of a granular medium flowing in such a geometry is not obvious
Dynamical diffraction in sinusoidal potentials: uniform approximations for Mathieu functions
Eigenvalues and eigenfunctions of Mathieu's equation are found in the short
wavelength limit using a uniform approximation (method of comparison with a
`known' equation having the same classical turning point structure) applied in
Fourier space. The uniform approximation used here relies upon the fact that by
passing into Fourier space the Mathieu equation can be mapped onto the simpler
problem of a double well potential. The resulting eigenfunctions (Bloch waves),
which are uniformly valid for all angles, are then used to describe the
semiclassical scattering of waves by potentials varying sinusoidally in one
direction. In such situations, for instance in the diffraction of atoms by
gratings made of light, it is common to make the Raman-Nath approximation which
ignores the motion of the atoms inside the grating. When using the
eigenfunctions no such approximation is made so that the dynamical diffraction
regime (long interaction time) can be explored.Comment: 36 pages, 16 figures. This updated version includes important
references to existing work on uniform approximations, such as Olver's method
applied to the modified Mathieu equation. It is emphasised that the paper
presented here pertains to Fourier space uniform approximation
Surface polaritons on left-handed cylinders: A complex angular momentum analysis
We consider the scattering of electromagnetic waves by a left-handed cylinder
-- i.e., by a cylinder fabricated from a left-handed material -- in the
framework of complex angular momentum techniques. We discuss both the TE and TM
theories. We emphasize more particularly the resonant aspects of the problem
linked to the existence of surface polaritons. We prove that the long-lived
resonant modes can be classified into distinct families, each family being
generated by one surface polariton propagating close to the cylinder surface
and we physically describe all the surface polaritons by providing, for each
one, its dispersion relation and its damping. This can be realized by noting
that each surface polariton corresponds to a particular Regge pole of the
matrix of the cylinder. Moreover, for both polarizations, we find that there
exists a particular surface polariton which corresponds, in the large-radius
limit, to the surface polariton which is supported by the plane interface.
There exists also an infinite family of surface polaritons of
whispering-gallery type which have no analogs in the plane interface case and
which are specific to left-handed materials.Comment: published version. v3: reference list correcte
A constitutive law for dense granular flows
A continuum description of granular flows would be of considerable help in
predicting natural geophysical hazards or in designing industrial processes.
However, the constitutive equations for dry granular flows, which govern how
the material moves under shear, are still a matter of debate. One difficulty is
that grains can behave like a solid (in a sand pile), a liquid (when poured
from a silo) or a gas (when strongly agitated). For the two extreme regimes,
constitutive equations have been proposed based on kinetic theory for
collisional rapid flows, and soil mechanics for slow plastic flows. However,
the intermediate dense regime, where the granular material flows like a liquid,
still lacks a unified view and has motivated many studies over the past decade.
The main characteristics of granular liquids are: a yield criterion (a critical
shear stress below which flow is not possible) and a complex dependence on
shear rate when flowing. In this sense, granular matter shares similarities
with classical visco-plastic fluids such as Bingham fluids. Here we propose a
new constitutive relation for dense granular flows, inspired by this analogy
and recent numerical and experimental work. We then test our three-dimensional
(3D) model through experiments on granular flows on a pile between rough
sidewalls, in which a complex 3D flow pattern develops. We show that, without
any fitting parameter, the model gives quantitative predictions for the flow
shape and velocity profiles. Our results support the idea that a simple
visco-plastic approach can quantitatively capture granular flow properties, and
could serve as a basic tool for modelling more complex flows in geophysical or
industrial applications.Comment: http://www.nature.com/nature/journal/v441/n7094/abs/nature04801.htm
Dragon-kings: mechanisms, statistical methods and empirical evidence
This introductory article presents the special Discussion and Debate volume
"From black swans to dragon-kings, is there life beyond power laws?" published
in Eur. Phys. J. Special Topics in May 2012. We summarize and put in
perspective the contributions into three main themes: (i) mechanisms for
dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii)
empirical evidence in a large variety of natural and social systems. Overall,
we are pleased to witness significant advances both in the introduction and
clarification of underlying mechanisms and in the development of novel
efficient tests that demonstrate clear evidence for the presence of
dragon-kings in many systems. However, this positive view should be balanced by
the fact that this remains a very delicate and difficult field, if only due to
the scarcity of data as well as the extraordinary important implications with
respect to hazard assessment, risk control and predictability.Comment: 20 page
Phenomenology and physical origin of shear-localization and shear-banding in complex fluids
We review and compare the phenomenological aspects and physical origin of
shear-localization and shear-banding in various material types, namely
emulsions, suspensions, colloids, granular materials and micellar systems. It
appears that shear-banding, which must be distinguished from the simple effect
of coexisting static-flowing regions in yield stress fluids, occurs in the form
of a progressive evolution of the local viscosity towards two significantly
different values in two adjoining regions of the fluids in which the stress
takes slightly different values. This suggests that from a global point of view
shear-banding in these systems has a common physical origin: two physical
phenomena (for example, in colloids, destructuration due to flow and
restructuration due to aging) are in competition and, depending on the flow
conditions, one of them becomes dominant and makes the system evolve in a
specific direction.Comment: The original publication is available at http://www.springerlink.co
Shift in herders’ territorialities from regional to local scale: the political ecology of pastoral herding in western Burkina Faso
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