A bead pack of more than
100,000 spheres. The system is a reconstruction by using the position
of the sphere
centres calculated from a 3D tomographic image
The same bead pack as in the
left picture but with the different colours indicating the topological
distance (number of links in the contact network) from a central sphere.
The science of granular
material has a
long history and in
the last few
years there has been a resurgence of interest in this field. Indeed,
much engineering literature is devoted to understanding how to deal
with these materials. Nevertheless, the technology for handling and
controlling granular materials is not as well developed as that for
handling other systems such as conventional fluids. Estimates suggest
that we waste 40% of the capacity of many industrial plants because of
problems encountered in dealing with these materials.
research subjects are sphere packing, sandpiles, vibrating grains, sand castle...
Our strength is the unique
- Leading expertises in the physics of complex and disordered
- Deep knowledge of disordered packing geometry;
- Ready acess to X-ray Computed Tomography facility;
- Cutting-edge reconstruction software;
- Acess to national supercomputer facilities;
- Innovative experimental methodology;
- Strong Numerical Simulation Competences.
X-ray Computed Tomography
We are ‘looking inside’ granular matter by using of
X-ray computed tomography. Our studies have produced an extensive
database for the grain coordinates of large granular aggregates at
different packing fractions. Such database has been used to perform
crucial analysis on the structure of granular matter at rest and on its
structural fluctuations during evolution. We investigate both the
static structure (geometrical structure; limiting densities; stress
propagation; mechanical behaviour) and the dynamical properties (flow,
avalanches, slow dynamics during compaction; size segregation; critical
slowdown, jamming and glass-transition; disorder-order transition and
crystallization). We established the existence of four density regions
we found the ‘structural parameters’ which enable to characterize the
structure at different packing fractions and different degrees of
STATISTICAL MECHANICS APPROACH
We have developed a deductive statistical mechanics
approach for granular materials which is formally built from only a few
realistic physical assumptions. The main result is the discovery of a
universal behaviour for the distribution of the density fluctuations.
Such a distribution is the equivalent of the Maxwell-Boltzmann's
distribution in the kinetic theory of gasses. The comparison with a
very extensive set of experimental and simulation data for packings of
monosized spherical grains, reveals a remarkably good quantitative
agreement with the theoretical predictions both at the grain level and
at the global system level. Such distributions are characterized by a
quantity (k) which is very sensitive to changes in the structural
organization. We demonstrate that k clearly reveals the occurrence of
DISCRETE ELEMENT METHOD (DEM) SIMULATIONS
Starting from the 3-dimesional images of the grain
packs obtained by X-ray computed tomography we perform "Virtual
Experiments" by reconstructing via DEM numerical samples of ideal
spherical beads with desired (and tunable) properties. The resulting
‘virtual packing’ has a structure that is almost identical to the
experimental one. However, from such a ‘virtual packing’ we can
calculate several static and dynamical properties (force network,
avalanches precursors, stress paths, stability, fragility,…) which are
otherwise not directly accessible via experiments. The simulations take
realistically into account non-linear Herzian repulsion, non-elastic
collisions, gravity and friction.
RANDOM APOLLONIAN PACKING (RRAP)
Apollonian packing has a long history dating back to
Apollonius of Perga (ca. 200B.C). This packing is formed by placing a
circular disc in the space between three mutually touching discs so
that it just touches the other three. The procedure is then continually
repeated, filling the new gaps generated by the addition of each new
disc. We have studied modern variations on this theme, in which grains
are sequentially placed at random positions in the pore space (Random
Apollonian Packing). We demonstrate the strong dependence of the
packing efficiency on the grain shape and observe that universal
relations exist between the grain shape and the fractal properties of
We have introduced the new Rotational Random Apollonian Packing (RRAP)
model, in which the grains are allowed to rotate during the packing
process. This additional degree of freedom allows the grains to pack
more densely. An
animation can be viewed here.
The relationship between the packing efficiency and the grain shape in
both the RAP and RRAP models can be understood by identifying the key
constraining length that limits the growth of grain during the packing
See also: http://www.garydelaney.net/rrap.html
(a) liquid rings trapped
contacts between grains;
(b) a bead pack of
spheres within a rubber balloon.
Avalanches in a rotating
simulation of a few
thousands spheres in a rectangular box.
(theory, simulations and statistical analysis)
Tim J. Senden
Tiziana Di Matteo (theory and
(numerical simulations and virtual experimets 2007-2008))
(numerical simulations, theory, 2005-2006)
Alexandre Kabla (experiment and
numerical study, 2004-2005)
Arthur Sakellariou (experiment, XCT
Stuart Ramsden ANUSF
(network theory and visualization)
Antonio Coniglio (University of Naples)
Georges Debrégeas (College de France, Paris)
Mario Nicodemi (University of
Matthias Schroeter (University of Texas at Austin)
Harry Swinney (University of
Texas at Austin)
(Trinity College Dublin)
M. Saadatfar (2002-2006)
C. Testa (2004, 2005)
dimensional beads packs
||T. Aste, "Insights into
Disorder'', (Oxford University Press, coming soon 2009).
|T. Aste and D.
Pursuit of Perfect Packing'', -Second Edition- (Taylor and Francis
London, 2008). (192 pages)
COMPLEX MATERIALS, Aste, T Di Matteo & A Tordesillas (Editors),
Lecture Notes in Complex Systems Vol.8 (World Scientific, Singapore
|T. Aste and D.
Pursuit of Perfect
Of Physics Publishing London 2000).
- Gary W Delaney , Stefan Hutzler and Tomaso Aste, “Relation
between grain shape and fractal properties in Random Apollonian
Packings with grain rotations”, Phys. Rev. Lett. 101 (2008) 120602.
- Melissa Jerkins, Matthias Schroter, Harry L. Swinney,Tim J.
Senden, Mohammad Saadatfar and Tomaso Aste, “Onset of mechanical
stability in random packings of frictional spheres”, Phys. Rev.
101 (2008) 018301.
- Iwan Schenker, Frank T. Filser, Tomaso Aste and Ludwig J.
and Mechanical Properties of Dense Particle Gels: Microstructural
Characterization”, J. Eur. Ceram. Soc., 2008, Vol. 28/7, pp
- T. Aste, T. Di Matteo “Emergence
distributions in granular materials and packing models”, Phys. Rev.
E 77 (2008) 021309 (8 pages).
- A.V. Anikeenko and N.N. Medvedev and T. Aste, “Structural and
entropic insights into the nature of random close packing limit”,
Phys. Rev E 77 (2008) 031101 (9 pages).
- T. Aste, G. Delaney and T. Di Matteo, "Understanding
complex matter from simple packing models", Proc. SPIE Vol. 6802,
68020E (Jan. 5, 2008). (keynote paper)
- Gary W. Delaney, Shio Inagaki, T. Di Matteo and Tomaso
Experiments on Complex Materials", Proc. SPIE Vol. 6802,
68020G (Jan. 5, 2008). (Invited Paper)
- Gary W. Delaney, Shio Inagaki and Tomaso Aste “Fine tuning
DEM simulations to perform virtual experiments with three-dimensional
granular packings”, Lecture Notes in Complex Systems Vol.8 (World
Scientific, Singapore 2007) 169 - 186.
- A.V. Anikeenko, N.N. Medvedev, T. Di Matteo, G. Delaney and
T. Aste, “Delaunay
simplex analysis of the structure of equal sized
sphere packings”, Lecture Notes in Complex Systems Vol.8 (World
Scientific, Singapore 2007) 27- 42.
- T. Aste, A. Tordesillas and T. Di Matteo, “The Science of
Complex Materials” Preface, World Scientific Lecture Notes in
Systems 8 (2007) vii – xi.
- T. Aste, T. Di Matteo, M. Saadatfar, T. J. Senden, Matthias
Schröter and Harry L. Swinney, “An invariant distribution in
granular media”, Euro Phys. Lett. 79 (2007) 24003 (5pp).
- T. Aste and T. Di Matteo “Correlations
statistics in granular packs” Eur. Phys. J. E 22 (2007), 235–240.
- T. Aste, “Volume
and geometrical constraints in granular packs”, Phys. Rev. Lett. 96
(2006) 018002. (arXiv:cond-mat/0408452,
- T. Aste, M. Saadatfar, T.J. Senden, “Local
relations between the number of contacts and density in monodisperse
sphere packs”, J. Stat. Mech. (2006) P07010.
- T. Aste and T. Di Matteo, “Nanometric
emergence of efficient non-crystalline atomic organization in
nanostructures”, Ed. R. H. J. Hannink and A. J. Hill, Chap. 2 in
“Nanostructure Control of Materials” (Woodhead Publishing Limited
Cambridge, 2006) 32-54.
- T. Aste, T. Di Matteo, “Materials and complexity:
emergence of structural complexity in sphere packings”, in Complex
Systems, Edited by Bender Axel, Proc. of SPIE, 6039 (2006) 6039G -17.
- T. Aste, M. Saadatfar , T.J. Senden, "The
of Disordered Sphere Packings", Phys. Rev. E. 71 (2005) 061302.
- T. Aste and T. Di Matteo, “The
13th problem”, The Australian Mathematical Society Gazette 32
- 50. T. Aste and T.J. Senden, "The
hierarchical properties of contact networks in granular packings",
Powders & Grains, H.J. Herrmann and S. McNamara (eds) (Taylor and
Francis, London 2005) 37-40. (arXiv:cond-mat/0504359, 2005).
- M. Saadatfar, A. Kabla, T. J. Senden and T. Aste, “The
geometry and the number of contacts of monodisperse sphere packs using
X-ray tomography”, Powders & Grains, H.J. Herrmann and S. McNamara
(eds) (Taylor and Francis, London 2005) 33-36.
- T. Aste, “Variations around disordered closed pakings”,
Journal of Physics Condensed Matter 17 (2005) S2361--S2390.
- T. Aste and U. Valbusa, “Ripples
and Ripples: from
Sandy Deserts to Ion-Sputtered Surfaces” New J. Phys. 7 (2005) 122.
- A. Sakellariou, T. J. Sawkins, A. Limaye, A. and T. J.
Tomography for Mesoscale Physics Applications", Physica A 339 152-158
- T. Aste and A. Coniglio, “Cell
theory for liquid solids and
glasses: from local packing configurations to global complex
behaviors”, Europhys. Lett. 67 (2004) 165-171.
- T. Aste and U. Valbusa, “Surface
instabilities in granular matter and ion-sputtered surfaces",
Physica A 332 (2004), 548-558.
- T. Aste, M. Saadatfar , A. Sakellariou, T.J. Senden, “Investigating
the Geometrical Structure of Disordered Sphere Packings” Physica
A 339 (2004) 16-23.
- T. Aste and A. Coniglio, “Cell
Approach to Glass Transition” Journal of Physics: Condensed Matter
15 (2003) S803-S811.
- T. Aste and A. Coniglio, “Glass
transition and local packings” Physica A, 330 (2003) 189-194.
- T. Aste, T. Di Matteo and E. Galleani d'Agliano, "Stress
transmission in granular matter", J. Phys. Condens. Matter. 14
(2002) 2391-2402. (cond-mat/0112311).
- T. Aste, "Circles,
and drops packings'', Phys. Rev. E 53 (1996), p.2571-79.
The data files containing the coordinates
of the sphere centres for some of the samples are available and must be
required directly to: tas110