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## Statistical mechanics of static granular media |

1Abdoulaye Fall and 1,2 Daniel Bonn 1 Van der Waals-Zeeman Institute University of Amsterdam
Valckenierstraat 65, 1018XE Amsterdam, The Netherlands 2 Laboratoire de Physique Statistique
Ecole Normale Supérieure 24 Rue Lhomond 75231 If one
stretches an auxetic material in one direction, it
will expand rather than retract in the other directions: it has a negative
Poisson ratio. However, only few examples of such materials are known. Under
shear rather than stretching, normal solids expand, although the effect is
small. Soft matter systems have in common that they show a large response to
relatively small applied stresses. Here we show that the effect of shear is
very large, and that contrary to expectation, foams and emulsions show a
fundamentally different normal response to shear: the foam tends to dilate,
whereas the emulsion contracts (akin to auxetic
behavior). We find that anomalous behavior in the response of the emulsion to
shear is triggered by the adhesivity between emulsion
droplets: if the adhesion is switched off, dilatant
behavior is observed. Thus, steric repulsions lead to
dilatancy whereas adhesion leads to contraction. ----
Creep Motion of a Granular Pile Induced by Thermal
Cycling Thibaut Divoux, Hervé Gayvallet,
and Jean-Christophe Géminard Université de Lyon, Laboratoire
de Physique, Ecole Normale Supérieure de Lyon, CNRS, 46
Allée d’Italie, 69364 Lyon cedex 07, We report a time-resolved study of the dynamics
associated with the slow compaction of a granular column submitted to thermal
cycles. The column height displays a complex behavior:
for a large amplitude of the temperature cycles, the
granular column settles continuously, experiencing a small settling at each
cycle. By contrast, for a small-enough amplitude, the column exhibits a
discontinuous and intermittent activity: successive collapses are separated by
quiescent periods whose duration is exponentially distributed. We then discuss
potential mechanisms which would account for both the compaction and the
transition at finite amplitude. ----
{1} Multi
Scale Mechanics, {2} NanoStructured Materials, DeftChemTech,
{3} PMMH,
UMR7636 (CNRS), The isotropic
compression of polydisperse packings
of frictionless spheres is modeled with the discrete element method (DEM). We investigate
the evolution
of coordination number as function of volume fraction for different system
parameters. The power law relationship, with power $\approx 1/2$, between
coordination number and density is confirmed in the jammed state for a broad
range of volume fractions and for different polydispersities.
Based on the discontinuity in the coordination number at the jamming point, we
find that polydispersity in the packing causes a
shift in the critical volume fraction, i.e., more heterogeneous packings jam at higher volume fractions. At higher
densities, neither the deformation history nor the loading rate
have a significant effect on the evolution of the coordination number.
However, for small densities the coordination number and the jamming volume
fraction do depend on both history and rate.Finally,
we propose and evaluate alternative methods to determine the critical volume
fraction based on the number of rattlers, the pressure and the ratio of kinetic
and potential energies. The results are all consistent with the critical
volume fractions obtained from the fits of the power law to the simulation
data. ---
Amorphous
solids of soft, frictionless particles close to (but above) their un-jamming
threshold (point J) have been shown to display interesting scaling properties
in their linear elastic properties. The same system in its fluid phase equally
displays nontrivial flow properties but little is known about the relation of
these properties to nearby point J and its isostatic
state. To fill this
gap, we employ a simulation technique that allows to take
a more detailed view on both, the elasticity of the solid and the flow of the
fluid, in one simulation. Implementing a quasistatic
simulation method we can study the borderline between fluid and solid state. We
generate a well defined ensemble of states that directly samples the system at
its yield-stress. We show that
at point J a continuous jamming transition from a freely-flowing state to a
yield-stress situation takes place, with the latter being characterized by the
same scaling properties as in linear elasticity. Approaching the transition from below we find
a diverging dynamical susceptibility. The associated particle mobilities show signs of strong spatial correlations, with
patterns involving string- and loop-like excitations as well as compact regions
of active particles. We propose to view the mechanical response as due to the
collective rearrangements of a liquid of long-lived "solid clusters".
At the jamming transition these clusters have the size of the system and
long-range elastic correlations start to dominate. In this regime, the system
yields through a different mechanism that is due to the presence of liquid-like
defects imbedded in a solid, elastic matrix. ---
Institution: Experimentalphysik V, Universität
Bayreuth, D-95440 Institution:
Max Planck Institute for Dynamics and Self-organization, D-37073 Adding a
certain amount of water to a pile of sand increases its mechanical stability
dramatically, leading to a material stiff enough for sculpturing sand castles.
This is due to the liquid bridges formed between adjacent particles which
introduce cohesion into the system. How the cohesive force changes the dynamics
of granular matter concerns the main topic of this study. First, recent
investigations on the phase diagram of wet granular matter under vertical
vibrations will be introduced. Focusing on the coexistence regime of fluid and
gas phases, the dynamics of granular 'gas bubbles' is presented, which suggests
the existence of interfacial tension between fluid and gas phases. Focusing on
the boundary between solid and fluid phases, we demonstrate experimentally that
fluidization is a surface melting process by utilizing ruby fluorescence. At
last, a newly built microwave radar setup for particle tracing in 3D will be
introduced. ---
Department of
Physics, We investigate
theoretically the jam formation in the initially homogeneous traffic flow by a
car-following model that emphasizes the short-range volume exclusion among
cars. Simulations are performed for the case of a single traffic lane, using a
periodic boundary condition. By applying various perturbations on speed and car
spacing, we observe a jam formation and its evolution toward a dynamic steady
state. It is shown from our model that traffic jam emerges over a critical
density of about 0.12 cars per meter. In this model traffic jams are exhibited
through at least two time scales, as these two relaxation time scales will be
investigated through different observables. ----
M. C. Jenkins
(1,2), M. D. Haw (1,3), W. C. K. Poon
(1), M. Schroeter (4), T. Aste
(5) and S. U. Egelhaaf (1,2) 1) SUPA, School of Physics, and
Collaborative Optical Spectroscopy, Micromanipulation and Imaging Centre
(COSMIC), The University of Edinburgh, James Clerk Maxwell Building, Kings
Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK. 2) Condensed Matter Physics Laboratory,
Heinrich-Heine-University, Universitaetstrasse 1,
40225 3) Department of Chemical and Process
Engineering, 4) Dynamics of Complex Fluids, Max Planck
Institute for Dynamics and Self-Organization, Bunsenstrasse
10, 37073 5) Applied Mathematics, Static
granular matter responds in a complex way to applied loads. Forces are transmitted inhomogeneously
through them, and depending on the preparation history, they can be stable
against gravity for a wide range of volume fractions. These phenomena require multi-particle,
cooperative effects, variously described as force chains, bridges, or arches.
However, an unambiguous characterisation is not
straightforward. One candidate is that
of Barker et al., who have found instances of bridges in simulated hard-sphere
granular systems. We have followed their
analysis in finding bridges in colloidal, nearly-colloidal, and granular
systems, where Brownian motion and gravity are present to different degrees. We have investigated bridge size
distributions in these different systems, and compared them with simulation
results. ---
We present rst results from a generalization of mode coupling theory (MCT)
to the nonequilibrium stationary state of a driven
granular fluid. In particular, we use MCT to calculate the coherent scattering
function F(q; t) = hq(0)jq(t)i.
One of the main features of MCT is the prediction of a glass transition, F(q; t ! 1) 6= 0, in dense equilibrium liquids. Extending
the mode coupling formalism to the nonequilibrium
regime, we can show that MCT predicts a glassy phase even for inelastic
granular systems. In leading order, the glass-transition singularity is not
invalidated by the driving. The main difference is,
that the glass transition is shifted to higher densities the more inelastic the
particles are. Consequently, the particles are more tightly localized in a granular
glass compared to an elastic hard sphere system. 1 Institut für Theoretische Physik, Universität Göttingen
Friedrich-Hund-Platz 1, 37077 Göttingen 2 Max Planck Institute für Dynamik und
Selbstorganisation, Bunsenstr. 10, 37073 Göttingen 3 Institut für Materialphysik im Weltraum, DLR, Linder
Höhe, 51147 Köln 1 ---
Institution: Van 't Hoff Laboratory for Physical and Colloid Chemistry, Debye
Institute for NanoMaterials, CH, Random packing
of non-spherical particles is of great importance for understanding the
properties and performance of composite materials, colloidal dispersions and
glasses, granular and porous media as well as fiber networks in biological
cells. Recently, we revealed a striking and non-intuitive behavior of
non-spherical granular packings - non-spherical
particles demonstrated the existence of a maximum in the packing density upon a
slight deviation from spherical shape. In the present study we investigate the
universality in the behavior of near-spheres and the dependence of the position
and the value of the maximum in the packing density on the system parameters.
Both mono- and poly-disperse non-spherical particles of various shapes such as sphero-cylinders, flat-faced cylinders, ellipsoids and
cut-spheres as well as their mixtures are considered by means of a statistical
geometry approach, computer simulations and experiments. We show that the
jamming mechanism of nearly spherical granular materials is fundamentally different
from that of spherical granular matter and of highly elongated. ---
Otto-von-Guericke
University Magdeburg, Germany Department for
Nonlinear Phenomena An experiment
is presented that extends the diversity of pattern forming phenomena found in
granular media. A flat container (Hele-Shaw cell) is
filled with a granular mixture and slowly rotated about its horizontal long
axis. The filling fraction is crucial for the observed effects. Rietz
& Stannarius: Phys. Rev. Lett.
100, 078002 (2008). http://141.44.47.63/w3fr/rotieren.html ---
Physics of
Fluids Group,
The dynamics
of particles floating on a Faraday wave is experimentally studied. For low
particle concentration it was shown [1] that, depending on wetting property and
density, the particles cluster either at the antinodes (maxima) or the nodes
(minima) of a standing Faraday wave. This separation is a single particle
effect. In the present study, the aim is to understand what happens when the
particle concentration is increased: Here we observe that particles that move
to the antinodes for low particle concentration form clusters at the nodes at
high concentrations. The explanation lies in the collective, attractive
capillary interaction among particles which counteracts the tendency of the
particles to move toward the antinodes. The transition between the two regimes
is studied as a function of the concentration and exhibits extremely long
transients. [1]
G. Falkovich ---
Elmar
Stärk {1}, Stefan Luding {2}
and Matthias Sperl - {1} Institut für Materialphysik im Weltraum, DLR, Köln {2} Universiteit Twente, The Netherlands Binary
mixtures are investigated at the transition from loose to load bearing packings. The transition is determined both in computer
simulation and experimentally in assemblies of stress-birefringent
particles. Both the size ratio of smaller to bigger particles as well as the
concentration of smaller particles is varied systematically. The transition is
determined accurately by observing a discontinuity in the number of contacts
per particle. It is found that the variation of transition density for
different mixing ratios follows three qualitatively different scenarios
depending on the size ratio of particles: For small size ratios there is a
minimum in the transition density, while for large size ratios there is a
maximum and for medium size ratios there are both a maximum and a minimum. This
non-trivial behaviour is very similiar
to recent predictions for the glass transition in binary mixtures. ---
Caballero-Robledo(2), Ko van der Weele(3), and Martin A.
van der Hoef(1)
(1) Faculty of
Science and Technology, (2) Centro de Investigacion en Materiales Avanzados S. C., Nuevo Leon, Mexico, (3) Department
of Mathematics, When a layer
of granular material is vertically shaken, the surface spontaneously breaks up
in a landscape of small Faraday heaps that merge into larger ones on an ever
increasing timescale. This coarsening process is studied in a linear setup, for
which the average lifetime of the transient state with $N$ Faraday heaps is
shown to scale as $N^{-3}$. We describe this process
by a set of differential equations for the peak positions; the calculated
evolution of the landscape is in excellent agreement with both the experiments
and simulations. The same model explains the observational fact that the number
of heaps towards the end of the process decreases approximately as $N(t) \propto t^{-1/2}$. ---
Multi Scale
Mechanics, TS, CTW, University of Twente, P.O. Box
217, 7500 AE Enschede, The Netherlands This research
will be at the junction of three areas: Implementation of Delaunay
Triangulation (DT) for contact detection, hierarchical data structures for
coarsening and micro-macro methods, and coupling of various techniques and
fields across the scales. In order to relate the micro parameters to macro, we
used an equivalent continuum model (EQM). The modeling
steps are as follow: ·
Choosing
a suitable representative volume element (RVE) of the nano
(micro)-structured material. ·
Replacing
the particles with nodes and connections with elements. ·
Developing
an equivalent-continuum model (ECM) of the RVE by equating the total strain
energies of the molecular and ECM, under identical loading conditions. ·
Calculating
the linear elastic parameters of the 3-D rod element such as stiffness and
cross sectional area at the micro level, and then mapping to nodes (particles).
·
Obtaining
linear elastic deformation of the particulate cubic structure by applying
appropriate boundary conditions (constant displacement). A DT is the
set of lines joining a set of points together such that each point is joined to
its nearest neighbors. It is the dual graph of the Voronoi
diagram (VD) and has a node for every Voronoi cell
and an edge between two nodes if the corresponding cells share an edge. Our idea is to
use DT not only for contact detections but also for creating particle
structures. Furthermore cluster detection is a possible application. ---
Peidong
Yu, Christian Krause,and
Matthias Sperl Institut für Materialphysik im Weltraum, DLR, 51170,
Köln, Germany Stress-birefringent materials are widely used in 2D granular
experiments and provide useful information on quantities like contact numbers,
force distribution, and force propagation. We show results on how to extend
this method to three dimensions. Different materials and production techniques are
demonstrated to yield a variety of tunable mechanical and optical properties in
3D granular particles. For these particles we report on the results of static
and dynamic measurements in dense granular assemblies. --- [Back] |