International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
International Workshop on PACKING PROBLEMS, 2-5 September 2012, Trinity College Dublin, Ireland.
Organizers: Prof. Stefan Hutzler (Trinity College Dublin) Dr. Adil Mughal (Aberystwyth University) Dr. Ho Kei Chan, Workshop Secretary (Trinity College Dublin)
Financial support:
Host:
1 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
Packing problems have a long and fascinating history, and the subject is active today on many fronts. The core of the subject presents us with idealized mathematical challenges, of which the most famous is the Kepler problem, while applications and implications span most of the sciences, engineering and industrial sectors (including pharmaceuticals and catalysis).
The modern study of packing problems makes use of diverse techniques drawn from computational and differential geometry, theory of minimal surfaces, and global optimization algorithms. As such the workshop will provide a unique opportunity for cross fertilization between a broad cross section of the scientific community ranging from mathematics to biology and computer science.
CONTENTS
1. Workshop Programme (Pg. 2 to Pg. 5), and Abstracts (Pg. 6 to Pg. 45)
2. List of participants (Pg. 46 to Pg. 48)
3. Web Access at Trinity College Dublin (Pg. 49)
4. Map of Dublin City Centre, and how to get there (Pg. 49)
5. Map of Trinity College Dublin (Pg. 50)
6. Accommodation near Trinity College Dublin (Pg. 51)
7. Things to do in Dublin (Pg. 51 to Pg. 56)
1. Workshop Programme, and Abstracts
Sunday, 2nd Sept 2012
WELCOME RECEPTION & REGISTRATION 17:00 20:00 (FITZGERALD LIBRARY)
2 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
Monday, 3rd Sept 2012
08:30 09:15 REGISTRATION (FITZGERALD LIBRARY)
Opening (Schrodinger Lecture Theatre) 09:15 09:30 SOME TRINITY PHYSICISTS THROUGH THE AGES Eric Finch Trinity College Dublin (Ireland)
Session A - General Packing Problems (Schrodinger Lecture Theatre) Chair: Tomaso Aste 09:30 10:00 A.1 PACKING PURSUITS (INVITED) Denis Weaire Trinity College Dublin (Ireland) A.2 SELF ASSEMBLY AND PACKING OF HARD 10:00 10:20 Michael Engel University of Michigan (USA) POLYHEDRA INTO COMPLEX STRUCTURES 10:20 10:40 A.3 WORST PACKING SHAPES Yoav Kallus Princeton University (USA) Coventry University (UK) & Johannes 10:40 11:00 A.4 REGULAR PACKINGS ON PERIODIC LATTICES Martin Weigel Gutenberg Universität Mainz (Germany)
11:00 11:20 COFFEE BREAK (FITZGERALD LIBRARY)
Session B - Packing of non-spherical particles (Schrodinger Lecture Theatre) Chair: Sascha Heitkam B.1 DENSE REGULAR PACKINGS OF IRREGULAR NON 11:20 12:00 Marjolein Dijkstra Utrecht University (The Netherlands) CONVEX PARTICLES (INVITED) B.2 STRONG INTERLOCKING OF NON CONVEX 12:00 12:20 François Ludewig University of Liège (Belgium) PARTICLES IN RANDOM PACKING B.3 RANDOM PACKINGS OF SPIKY PARTICLES: 12:20 12:40 Pierre M. Adler UPMC (France) GEOMETRY AND TRANSPORT PROPERTIES B.4 ENTROPY DRIVEN CRYSTALLIZATION IN DENSE Nikos Ch. Universidad Politécnica de Madrid 12:40 13:00 SYSTEMS OF ATHERMAL CHAIN MOLECULES Karayiannis (Spain)
13.00 14.20 LUNCH (BUTTERY FOOD COURT)
Session C - Packing of granular matter (Schrodinger Lecture Theatre) Chair: Matthias Möbius 14:20 14:40 C.1 - PRECISELY CYCLIC SAND (INVITED) Paul Chaikin New York University (USA) Friedrich Alexander Universität / 14:40 15:00 C.2 FRACTAL SUBSTRUCTURE OF A NANOPOWDER Thorsten Pöschel Universität Erlangen Nürnberg (Germany) C.3 DILATANCY IN GRANULAR MEDIA UNDER SHEAR: Institut de Physique et Chimie des 15:00 15:20 Nick Rivier A ROUTE TO CLOSER PACKING? Matériaux de Strasbourg (France) C.4 PATTERN FORMATION IN CONTINUOUSLY AGITATED Otto von Guericke University 15:20 15:40 Frank Rietz TWO DIMENSIONAL PACKINGS (Germany)
15:40 16:00 COFFEE BREAK (FITZGERALD LIBRARY)
Session D - Packing of foams, and related partitioning problems (Schrodinger Lecture Theatre) Chair: Ho Kei Chan D.1 HEXAGONAL OR CIRCULAR? PACKING A FINITE 16:00 16:20 Simon Cox Aberystwyth University (UK) COLLECTION OF DEFORMABLE OBJECTS D.2 FROM CLUSTERS OF PARTICLES TO 2D BUBBLE 16:20 16:40 Edwin Flikkema Aberystwyth University (UK) CLUSTERS 16:40 17:00 D.3 CRYSTALLINE POLYHEDRAL FOAM COLUMNS Stefan Hutzler Trinity College Dublin (Ireland) D.4 A PLANAR PARTITIONING PROBLEM: DIVIDING A 17:00 17:20 Antonio Cañete Universidad de Sevilla (Spain) PLANAR DISK INTO REGIONS OF PRESCRIBED AREAS
WORKSHOP DINNER 19:00 22:00 (MESSRS MAGUIRES, BURGH QUAY, DUBLIN 2)
3 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
Tuesday, 4th Sept 2012
Session E - General problems in sphere packing (Schrodinger Lecture Theatre) Chair: Denis Weaire 09:00 09:40 E.1 RANDOM PACKING BEFORE THE ARK (INVITED) John Finney University College London (UK) E.2 - THERMODYNAMIC STATUS OF RANDOM CLOSE 09:40 10:20 Les Woodcock University of Manchester (UK) PACKING (INVITED) 10:20 10:40 E.3 SPHERE PACKINGS AND CRYSTAL CHEMISTRY Michael O’Keeffe Arizona State University (USA)
10:40 11:00 COFFEE BREAK (FITZGERALD LIBRARY)
Session F - Packing of equal-sized spheres (Schrodinger Lecture Theatre) Chair: Stefan Hutzler F.1 WHY DO SPHERES PREFER FCC PACKING WHEN Institut für Strömungsmechanik (Ger.) 11:00 11:40 Sascha Heitkam SUBJECTED TO EXTERNAL FORCES? (INVITED) & U. Paris Sud XI, Orsay (France) F.2 DENSEST COLUMNAR PACKINGS OF HARD SPHERES 11:40 12:00 Ho Kei Chan Trinity College Dublin (Ireland) FROM SEQUENTIAL DEPOSITION F.3 PHYLLOTACTIC DESCRIPTION OF HARD SPHERE 12:00 12:20 Adil Mughal Aberystwyth University (UK) PACKING IN CYLINDRICAL CHANNELS F.4 HIGH DENSITY PACKINGS OF EQUAL CIRCLES IN Otto von Guericke University of 12:20 12:40 Eckard Specht RECTANGLES WITH VARIABLE ASPECT RATIO Magdeburg (Germany) F.5 PACKING CONFINED HARD SPHERES DENSER WITH Heinrich Heine Universität Düsseldorf 12:40 13:00 Erdal C. Oğuz NEW PRISM PHASES (Germany)
13.00 14.20 LUNCH (BUTTERY FOOD COURT)
Session G - Packing of polydisperse spheres (Schrodinger Lecture Theatre) Chair: Ho Kei Chan G.1 A SIMPLE GRANOCENTRIC MODEL FOR PACKING OF 14:20 14:40 Maxime Clusel Universite Monptellier (France) POLYDISPERSE SPHERES G.2 UNIVERSAL CORRELATIONS IN POLYDISPERSE 14:40 15:00 Cathal O’Donovan Trinity College Dublin (Ireland) FRICTIONLESS DISORDERED PACKINGS G.3 MEAN FIELD APPROXIMATION OF POLYDISPERSE 15:00 15:20 Vitaliy Ogarko University of Twente (The Netherlands), HARD SPHERE MIXTURES BY TRIDISPERSE SYSTEMS
15:20 15:40 COFFEE BREAK (FITZGERALD LIBRARY)
Session H - Other problems in sphere packing (Schrodinger Lecture Theatre) Chair: Adil Mughal H.1 THE SHAPE OF THE VORONOI CELLS INSIGHT Gerd Schroeder Friedrich Alexander Universität 15:40 16:20 INTO SPHERICAL BEAD PACKS (INVITED) Turk (Germany) H.2 NON UNIFORMITIES IN THE PACKING PROPERTIES OF Friedrich Alexander Universität / 16:20 16:40 Nikola Topic Universität Erlangen Nürnberg LARGE HEAPS OF GRANULAR MATTER (Germany)
16:40 18:30 DISCUSSIONS (FITZGERALD LIBRARY)
18:30 19:00 DRINKS RECEPTION (SCIENCE GALLERY)
Session I - Public Lecture (Paccar Theatre, Science Gallery) Chair: Stefan Hutzler I - EXPERIMENTAL GEOMETRY: EXPERIMENTS WITH 19:00 19:50 Paul Chaikin New York University (USA) CANDIES, DICE AND COLLOIDS (INVITED)
4 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
Wednesday, 5th Sept 2012
Session J - Methods of characterizing packings (Schrodinger Lecture Theatre) Chair: Simon Cox J.1 AUTOREFERENTIAL ORDER: AN INFORMATION 09:00 09:40 THEORETIC APPROACH TO ENCODE DISORDERED Tomaso Aste University College London (UK) STRUCTURES (INVITED) J.2 GETTING RANDOM CLOSE PACKINGS OF CONVEX Jean François 09:40 10:00 University of Bristol (UK) POLYHEDRA Camenen J.3 A COMPLEX NETWORK APPROACH TO THE Università Federico II di Napoli 10:00 10:20 Roberto Arévalo EQUILIBRIUM STATES IN GRANULAR PACKING (Italy) J.4 SIZE TOPOLOGY RELATIONS: DISORDER IN TILINGS University of Illinois at Urbana 10:20 10:40 Sascha Hilgenfeldt AND PACKINGS Champaign (USA)
10:40 11:00 COFFEE BREAK (FITZGERALD LIBRARY)
Session K - X-ray characterization of packings (Schrodinger Lecture Theatre) Chair: Stefan Hutzler 11:00 11:20 K.1 TOMOGRAPHY OF MONODISPERSE LIQUID FOAMS Aaron Meagher Trinity College Dublin (Ireland) K.2 APPLICATIONS OF X RAY IMAGING TECHNOLOGY IN Shanghai Jiao Tong University 11:20 11:40 Yujie Wang GRANULAR PHYSICS (China)
Concluding remarks (Schrodinger Lecture Theatre) 11:40 12:00 Adil Mughal Aberystwyth University (UK)
12:00 14:00 LUNCH (BUTTERY FOOD COURT)
5 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
A.1 (Invited Talk)
PACKING PURSUITS
Denis Weaire School of Physics, Trinity College Dublin, Dublin 2, Ireland Email: [email protected]
The history of some ideas about packing will be sketched, including in particular those of Reynolds, Kelvin and Bernal.
References Aste T. and Weaire D. (eds.) (2008), The Pursuit of Perfect Packing (2nd Edition) , CRC Press, Taylor and Francis.
6 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
A.2 (Oral)
SELF ASSEMBLY AND PACKING OF HARD POLYHEDRA INTO COMPLEX STRUCTURES
Michael Engel (1,#), Pablo F. Damasceno(1,2) and Sharon C. Glotzer(1,2,3) (1) Department of Chemical Engineering, (2) Applied Physics Program, and (3) Department of Mechanical Science and Engineering, University of Michigan, Ann Arbor, Michigan, 48109, U. S. A.. # Email: [email protected]
The last years have seen great progress in improving the lower bounds for densest packings of tetrahedra and other anisotropic particles. At the same time many novel ordered phases, some structurally highly complex, have been discovered. This presentation focuses on isolating the role of building block geometry for self assembly and packing. We demonstrate how novel and unusual crystal structures can be achieved solely with anisotropic shape. From simple measures of particle geometry and local order in the fluid, the assembly of a given polyhedron into either a liquid crystal, plastic crystal, or crystal can be predicted. We also compare the assembled structures with densest packings of the building blocks and show that good packings can often be distinct from what is observed to assemble from the disordered state. This suggests that dense packings may not always be illustrative of what is achievable in experiment, for example with colloids.
References
Chen E. R., Engel M. and Glotzer S. C., "Dense crystalline dimer packings of regular tetrahedra", Disc. Comp. Geom. 44, 253 (2010)
Damasceno P. F., Engel M. and Glotzer S. C., "Crystalline assemblies and densest packings of a family of truncated tetrahedra and the role of directional entropic forces", ACS Nano 6, 609 (2012)
Damasceno P. F., Engel M. and Glotzer S. C., "Predictive self assembly of polyhedra into complex structures", in press [arXiv:1202.2177] (2012)
Haji Akbari A., Engel M., et al. , "Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra", Nature 462, 773 (2009)
Haji Akbari A., Engel M. and Glotzer S. C., "Phase diagram of hard tetrahedra", J. Chem. Phys. 135, 194101 (2011)
7 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
A.3 (Oral)
WORST PACKING SHAPES
Yoav Kallus (1,#) and Fedor Nazarov (2) 1. Princeton Centre for Theoretical Sciences, Princeton University, U. S. A. 2. Department of Mathematical Sciences, Kent State University, U. S. A. # Email: [email protected]
The question of which convex shapes leave the most empty space in their densest packing is the subject of Reinhardt's conjecture in two dimensions and Ulam's conjecture in three dimensions. In two dimensions, a regular octagon whose corners have been smoothed to arcs of hyperbolas is known to be a local minimum of the optimal packing fraction. In three dimensions, we show that the ball is similarly a local minimum: it is the worst packing shape among sufficiently spherical shapes. Additionally, we discuss the situation in higher dimensions and the possibility of using these “local” results to obtain “global” ones via a branch and bound computation.
8 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
A.4 (Oral)
REGULAR PACKINGS ON PERIODIC LATTICES
Tadeus Ras (1), Rolf Schilling (2) and Martin Weigel (2,3,#) 1. Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany 2. Institut für Physik, Johannes Gutenberg Universität Mainz, 55127 Mainz, Germany 3. Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, U. K. # Email: [email protected]
We investigate the problem of packing identical hard objects on regular lattices in d dimensions. Restricting configuration space to parallel alignment of the objects, we study the densest packing at a given aspect ratio X. For rectangles and ellipses on the square lattice as well as for biaxial ellipsoids on a simple cubic lattice, we calculate the maximum packing fraction. It is proved to be continuous with an infinite number of singular points. In two dimensions, all maxima have the same height, whereas there is a unique global maximum for the case of ellipsoids. The form of maximum packing fraction as a function of aspect ration is discussed in the context of geometrical frustration effects, transitions in the contact numbers and number theoretical properties. Implications and generalizations for more general packing problems are outlined [Ras, 2011].
Figure 1: Maximum packing configurations of ellipses with aspect ratios X=3 (green, bottom), X = 4.4...(blue, middle), and X=6 (red, top).
References Ras T., Schilling R. and Weigel M., Physical Review Letters 107, 215503 (2011).
9 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
B.1 (Invited Talk)
DENSE REGULAR PACKINGS OF IRREGULAR NONCONVEX PARTICLES
Joost de Graaf (1), Ren é van Roij (2), and Marjolein Dijkstra (1,#) (1) Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands (2) Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands # Email: [email protected]
We present a new numerical scheme to study systems of nonconvex, irregular, and punctured particles in an efficient manner. We employ this method to analyze regular packings of odd shaped bodies, both from a nanoparticle and from a computational geometry perspective. Besides determining close packed structures for 17 irregular shapes, we confirm several conjectures for the packings of a large set of 142 convex polyhedra and extend upon these. We also prove that we have obtained the densest packing for both rhombicuboctahedra and rhombic enneacontrahedra and we have improved upon the packing of enneagons and truncated tetrahedra.
10 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
B.2 (Oral)
STRONG INTERLOCKING OF NON CONVEX PARTICLES IN RANDOM PACKING
François Ludewig (#), Eric Opsomer and Nicolas Vandewalle GRASP, Physics Department, University of Liège, B 4000 Liège, Belgium # Email: [email protected]
We investigate numerically the properties of piles composed by non convex grains that are built by the agglomeration of spheres [Ludewig, 2012]. The sphericity £p is used as key parameter to describe the shape of these grains. The measurement of contact and coordination number emphasizes the difficulty to describe a pile that is composed by non spherical particles. The study of the force distribution in the packing reveals that the interlocking induces multiple contacts and increases the stability of the pile. In the opposite, the same phenomenon is responsible for the low volume fraction of the pile. The well know relations between the classic parameters, that are used to characterise a pile, are no longer valid in the case of complex particles.
References Ludewig F. and Vandewalle N., Phys. Rev. E 85 , 051307 (2012).
11 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
B.3 (Oral)
RANDOM PACKINGS OF SPIKY PARTICLES: GEOMETRY AND TRANSPORT PROPERTIES
I. Malinouskaya (1), V. V. Mourzenko (2), J. F. Thovert (2) and P. M. Adler (1,#) 1. UPMC, France 2. Institut P', France # Email: [email protected]
Random packings of grains can be found in various natural environments as well as in industrial applications and they are a very interesting topic for scientific research due to their very complex behaviour. Most earlier works were devoted to random packings of spheres, whether they are mono or polydisperse and the studies devoted to nonspherical particles are much less common and are mostly experimental.
The purpose of this talk is to study the packings of star particles which are not convex. Each grain is obtained by addition to a sphere of one or more identical ellipsoids with the same center. Examples of these particles are given in Figures 1a and b. Because of their general aspect, these particles are called spiky. Since they are yet nearly unexplored, there is a fundamental interest in the study of the properties of non convex grain packings. In addition, the kind of particles considered here is reminiscent of various objects such as grafted particles, some pellets, flakes or small grain clusters. Therefore, the present results can find applications in a variety of industrial situations.
The generation of the spiky particles, the various shapes which were studied and the sequential algorithm which is used are described first. An example of packing is provided in Figure 1c. The geometrical properties of the particles such as the volume, the surface and the sphericity index are presented. Collective properties of the packings are also studied, namely porosity, hydraulic radius, correlation functions and orientation.
Then, transport properties are studied. The macroscopic conductivity is derived by solving the Laplace equation. Permeability is obtained by solving the Stokes equations.
Overall correlations are proposed to approximate these properties as functions of the grain equivalent size and sphericity index.
(a) (b) (c) Figure 1: Elementary non convex particles in (a) and (b). (c) Packing of particles.
12 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
B.4 (Oral)
ENTROPY DRIVEN CRYSTALLIZATION IN DENSE SYSTEMS OF ATHERMAL CHAIN MOLECULES
Nikos Ch. Karayiannis (#1), Katerina Foteinopoulou and Manuel Laso (#2)
Institute for Optoelectronics and Microsystems (ISOM) and ETSII, Universidad Politécnica de Madrid (UPM), José Gutiérrez Abascal 2, 28006 Madrid, Spain. #1 Email: [email protected] #2 Email: [email protected]
We describe the direct observation of entropy driven crystallization in simulations of dense packings of linear hard sphere chains. Crystal nuclei form spontaneously in the phase coexistence region independently of chain length. Incipient nuclei consistently develop well defined, stack faulted layered morphologies with a single stacking direction. These morphologies deviate markedly from those of monomeric analogs. The ordering transition is driven by the increase in translational entropy: ordered sites exhibit enhanced mobility as their local free volume becomes more spherical and symmetric.
References [1] Karayiannis N. and Laso M., “Dense and nearly jammed random packings of freely jointed chains of tangent hard spheres”, Physical Review Letters 100 , 050602 (2008). [2] Karayiannis N. Ch. and Laso M., “Monte Carlo Scheme for Generation and Relaxation of Dense and Nearly Jammed Random Structures of Freely Jointed Hard Sphere Chains” Macromolecules 41 , 1537 1551 (2008). [3] Karayiannis N. and Laso M., "Flexible chain molecules in the marginal and concentrated regimes: universal static scaling laws and cross over predictions", Journal of Chemical Physics 128 , 174901 (2008). [4] Foteinopoulou K., Karayiannis N. Ch., Laso M., Kröger M. and Mansfield M., “Universal Scaling, Entanglements, and Knots of Model Chain Molecules”, Physical Review Letters 101 , 265702 (2008). [5] Karayiannis N., Foteinopoulou K., Laso M. and Kröger M., "Structure, Dimensions and entanglement statistics of long linear polyethylene chains", Journal of Physical Chemistry B 113 , 442 455 (2009). [6] Karayiannis N., Foteinopoulou K. and Laso M., “The characteristic crystallographic element norm: a descriptor of local structure in atomistic and particulate systems”, Journal of Chemical Physics 130, 074704 (2009). [7] Laso M., Karayiannis N. Ch., Foteinopoulou K., Kröger M. and Mansfield M., “Maximally random jammed packings of hard–sphere chain molecules: universal scaling, entanglement and knotting”, Soft Matter 5, 1762–1770 (2009). [8] Karayiannis N., Foteinopoulou K. and Laso M., “The structure of maximally random jammed packings of freely jointed chains of tangent hard spheres” Journal of Chemical Physics 130 , 164908 (2009). [9] Karayiannis N., Foteinopoulou K. and Laso M., “Contact network in nearly jammed disordered packings of hard sphere chains”, Physical Review E 80 , 011307 (2009). [10] Karayiannis N., Foteinopoulou K. and Laso M., “Entropy driven crystallization in dense systems of athermal chain molecules”, Physical Review Letters 103 , 045703 (2009). http://focus.aps.org/story/v24/st5 [11] Karayiannis N., Foteinopoulou K., Abrams C. F. and Laso M., “Modeling of crystal nucleation and growth in athermal polymers: self assembly of layered nano morphologies”, Soft Matter 6, 2160 2173 (2010). [12] Karayiannis N., Malshe R., de Pablo J. J. and Laso M., “Fivefold symmetry as an inhibitor to hard sphere crystallization ”, Phys. Rev. E 83 , 061505 (2011). [13] Karayiannis N., Malshe R., Kröger M., de Pablo J. J. and Laso M., “Evolution of fivefold local symmetry during crystal nucleation and growth in dense hard sphere packings”, Soft Matter 8, 844 858 (2012).
13 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
C.1 (Invited Talk)
PRECISELY CYCLIC SAND
John Royer and Paul Chaikin (#) Centre for Soft Matter Research, New York University, New York, USA. #Email: [email protected] / [email protected]
Self organization under periodic driving is a common feature in many disparate far from equilibrium systems. One of the simplest examples is a suspension under cyclic shear, which exhibits a phase transition from a fluctuating state to a reversible state after particles arrange themselves to avoid collisions. While there has been substantial interest in granular packs and their response to shear, the range of accessible states and factors governing self organization are not well established. Using numerical simulations we show that cyclic shear of a granular material leads to dynamic self organization into several different phases. We present a phase diagram in strain – friction space which shows chaotic dispersion, crystal formation, vortex patterns and most unusually a disordered limit cyclic in which each particle precisely retraces a different path from other particles making and breaking many contact in each cycle.
14 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
C.2 (Oral)
FRACTAL SUBSTRUCTURE OF A NANOPOWDER
Thomas Schwager (1), Dietrich E. Wolf (2), Nikola Topic (3), Thorsten Pöschel (3,#) 1. Bruker Nano GmbH, Berlin, Germany 2. Universität Duisburg Essen, Fachbereich Physik, Duisburg, Germany 3. Universität Erlangen Nürnberg, Germany # Email: [email protected] erlangen.de
The structural evolution of a nanopowder by repeated dispersion and settling can lead to characteristic fractal substructures with robust statistical properties. This is shown by numerical simulations of a two dimensional model agglomerate of adhesive rigid particles. The agglomerate is cut into fragments of a characteristic size l, which then are settling under gravity. Repeating this procedure converges to a loosely packed structure, the properties of which are investigated: (a) The final packing density is independent of the initialization, (b) the short range correlation function is independent of the fragment size, (c) the structure is fractal up to the fragmentation scale l, and (d) the relaxation time increases linearly with l.
Figure 1: Asymptotic structure of the sediment after many iterations: homogeneous on the long scale, fractal on the short scale
References T. Schwager, D. E. Wolf, and T. P ̈oschel, ”Fractal Substructure of a Nanopowder”, Phys. Rev. Lett., 100: 218002, 2008. D. E. Wolf, T. Pöschel, T. Schwager, A. Weuster, and L. Brendel, ”Fractal Substructures due to Fragmentation and Reagglomeration” in M. Nakagawa and S. Luding (eds.), ”Powders and Grains 2009”, Springer (2009).
15 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
C.3 (Oral)
DILATANCY IN GRANULAR MEDIA UNDER SHEAR: A ROUTE TO CLOSER PACKING?
N. Rivier (#) and J. Y. Fortin Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504 ULP CNRS, 23 rue du Löss, BP 43, 67034 Strasbourg cedex 2, France # Email: [email protected] strasbg.fr
The apparent paradox of dilatancy was pointed out by O. Reynolds in 1885, to the amazement of Lord Kelvin and the puzzlement of many lesser mortals ever since. It is explained simply in a minimal model of the granular material ("sand") as hard spheres with infinite tangential friction, packed together as tetrahedral and making up a graph. Upon external stress, the spheres can either roll on each other without slip impossible in circuits of odd numbers of grains in contact , or lose contact with each other. Uniaxial stress (the vertical foot's pressure) shears the granular material; it forces the grains to roll on each other and the odd circuits to open up. Each tetrahedron of spheres distorts to break the triangular circuits of grains in contact, thereby increasing its volume and letting in water that is expelled in the wet footprint left behind.
How do the tetrahedra pack together? Is the distortion transmitted consistently from one tetrahedron to the next? Can disorder be accommodated? The answers are in looking at polytopes, close packed in positively curved space and very good approximation of the local environment in Euclidean 3D space. Notably, the distortion can cause topological transformations that may produce closer packing (topological annealing).
The actual transformation path followed by the spheres is the same as that of the atoms in a martensite transformation in iron and steel, that is a displacive transformation (analogous, locally, to the motion of dislocations) but it is done here with hard spheres instead of atoms. The granular material behaves as an auxetic material (material with negative Poisson's ratio, as in some knitting patterns) with the diagonal struts of two spheres in contact providing here the rigid elements hinged on each other. This behaviour is obtained by iterating polytope {3,3,4} in the same fashion as a geodesic dome can be built from (half of) an icosahedron {3,5}.
16 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
C.4 (Oral)
PATTERN FORMATION IN CONTINUOUSLY AGITATED TWO DIMENSIONAL PACKINGS
Frank Rietz Department for Nonlinear Phenomena, University Magdeburg, Germany, and Max Planck Institute for Dynamics and Self Organization Goettingen, Germany Email: [email protected]
Self organized pattern formation in two dimensional packings is reported. After continuous agitation of a particle monolayer, two possible states were observed: (1) The packing segregates without any recognizable collective particle motion, or (2) the packing stays mixed and the particles move in regular convection rolls. The system is in some respect similar to convection in rotating flat containers [1].
The packing is periodically jammed and unjammed by back and forth sliding of the beads. One might expect an erratic motion. Surprisingly, the particles move under certain circumstances in multiple convection rolls. The number of rolls is determined by the aspect ratio of the confining borders. Irrespective of some superficial similarity to convection in shaken systems, the driving mechanism is completely different, and only partially understood. Because of the simplicity of the experiment a theoretical description might be accessible.
References [1] F. Rietz and R. Stannarius. ”Convection and segregation in a flat rotating sandbox.” New J. Phys. 14 015001 (2012).
17 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
D.1 (Oral)
HEXAGONAL OR CIRCULAR? PACKING A FINITE COLLECTION OF DEFORMABLE OBJECTS
Simon Cox IMAPS, Aberystwyth University, U. K. Email: [email protected]
How should equal sized deformable objects best be packed so as to minimize the amount of interface? In 3D this is known as the Kelvin problem, and in 2D it is solved by the hexagonal honeycomb, the least perimeter way to divide the plane into regions of unit area. I will describe the finite case in 2D, where the interest is in determining the shape of the periphery of a cluster of N equal area deformable "bubbles" that minimizes the total perimeter. I will provide numerical evidence for N up to 10^5 that disproves the conjecture that for N a hexagonal number the optimal cluster should be cut from the hexagonal lattice. This suggests that as N tends to infinity, the dominance of the hexagonal lattice in the bulk does not extend to the periphery, and that circular clusters may be optimal. This is joint work with Frank Morgan and Francois Graner, see arxiv:1206.3858.
18 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
D.2 (Oral)
FROM CLUSTERS OF PARTICLES TO 2D BUBBLE CLUSTERS
Edwin Flikkema (#) and Simon Cox Institute of Mathematics and Physics, Aberystwyth University, Penglais, Aberystwyth, SY23 3BZ, United Kingdom # Email: [email protected]
In this presentation the analogy between 2D interacting particle systems and 2D clusters of bubbles is explored.
In cluster physics a cluster is often modelled as a set of particles that interact via potentials, thus resulting in a Potential Energy Surface (PES). Minima on the PES correspond to stable cluster geometries. An important problem in cluster physics is locating low lying minima, and more specifically the global minimum. Basin Hopping is a global optimisation method that has been particularly successful in finding the global minima of clusters such as those with the Lennard Jones potential.
In this presentation we propose to use two dimensional cluster geometries as starting points for finding the minimal perimeter configuration of two dimensional clusters of bubbles. A Voronoi partition is used to turn a 2D pattern of particles into a 2D set of cells (see figure 1). Surface evolver is then used to minimize the perimeter for fixed, equal, bubble areas. Free bubble clusters have been considered, as well as clusters confined within a shape such as a circle or a polygon [Cox, 2010]. Various forms of the interaction potential have been compared and their success in producing good candidates for the bubble cluster problem has been monitored.
Figure 1: Procedure for generating bubble clusters starting from particle clusters.
References Cox S. J. and Flikkema E., The Electronic Journal of Combinatorics, 17(1):R45, 2010.
19 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
D.3 (Oral)
CRYSTALLINE POLYHEDRAL FOAM COLUMNS
Stefan Hutzler School of Physics, Trinity College Dublin, Dublin 2, Ireland Email: [email protected]
Soap bubbles of equal volume readily crystallise as ordered polyhedral foam structures when introduced into tubes whose width is of the same order as the bubble diameter. We review the different types of structures that occur in tubes of circular, square and triangular cross section and compare with results from computer simulations using Ken Brakke's Surface Evolver software.
References Tobin S. T., Barry J. D., Meagher A. J., Bulfin B., O'Rathaille C. E. and Hutzler S. (2011), Ordered polyhedral foams in tubes with circular, triangular and square cross section < http://dx.doi.org/10.1016/j.colsurfa.2010.11.024 >, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 382, 24 31.
20 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
D.4 (Oral)
A PLANAR PARTITIONING PROBLEM: DIVIDING A PLANAR DISK INTO REGIONS OF PRESCRIBED AREAS
Antonio Cañete Dpto. Matematica Aplicada I, Ets Ing. Informatica, Campus de Reina Mercedes, Universidad de Sevilla Email: [email protected]
In this work we study the isoperimetric problem of dividing a planar disk into n regions of given areas, using the least possible perimeter. The general approach of this problem allows regions to be disconnected, which implies that a wide range of possible partitions have to be taken into account. Due to the regularity conditions (Plateau¡¦s laws) and some geometric reasonings, we find the solutions for n=2 and n=3 , and solve partially the case n=4 .
Least perimeter partitions of the disk for two and three regions of prescribed areas
References Cañete A. and Ritore M., Least perimeter partitions of the disk into three regions of given areas , Indiana Univ. Math. Journal, 2004. Cañete A., Least perimeter partitions of the disk , Proceedings of the XIII Fall Workshop on Geometry and Physics (RSME), 2005.
21 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
E.1 (Invited Talk)
RANDOM PACKING BEFORE THE ARK
John Finney Department of Physics & Astronomy, & London Centre for Nanotechnology, University College London, London, U. K. Email: [email protected]
In the 1950s and 1960s, liquids were generally regarded as either dense gases or disordered solids, and theoretical attempts at understanding their structures and properties were largely based on those concepts. J.D. Bernal, himself a crystallographer, was unhappy with either approach, preferring to regard simple liquids as “homogeneous, coherent and essentially irregular assemblages of molecules containing no crystalline regions”. He set about realizing this conceptual model through a detailed examination of the structures and properties of random packings of spheres.
In order to test the relevance of the model to real liquids, ways had to be found to realize and characterize random packings. This was at a time when computing was slow and in its infancy, so he and his collaborators set about building such models in the laboratory, and examining aspects of their structures in order to try to characterize them in ways which would enable useful comparison with the properties of real simple liquids. Some of the (often time consuming and frustrating) routes followed to build and characterize random packings will be described, as well the comparisons made with the measured properties of simple liquids.
With the increase of the power and availability of computers towards the end of the 1960s, computational approaches became increasingly exploited in random packing studies. This enabled amongst other things the use of packing concepts, and the tools developed to characterize them, in understanding systems as diverse as metallic glasses, crystal liquid interfaces, protein structures, enzyme substrate interactions and the distribution of galaxies, as well as their exploitation in, for example, oil extraction, understanding chromatographic separation columns, and packed beds in industrial processes.
22 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
E.2 (Invited Talk)
THERMODYNAMIC STATUS OF RANDOM CLOSE PACKING
Les Woodcock Manchester Interdisciplinary Biocentre, University of Manchester, U. K. Email: [email protected]
A state of random close packing (RCP) of spheres has been found to have a thermodynamic status and a central role in the description of equilibrium liquids, metastable supercooled liquids, and even supercritical “liquids” [1]. The RCP limiting density, with well characterized structure, can be produced by both irreversible and reversible processes which establish a thermodynamic status. Alongside recent findings that the Mayer cluster integral expansion cannot represent dense fluid equations of state beyond low density percolation transitions, this means RCP belongs to the same thermodynamic phase as the equilibrium liquid, up to and beyond the recently discovered temperature of a “line of critical states”. Since, for any molecular Hamiltonian, the thermodynamic state functions on Gibbs surfaces are continuous in all the derivatives with respect to state variables, within the phase bounds, it follows that all real liquids must also have a well defined thermodynamic amorphous ground state (AGS) at temperatures approaching absolute zero. The AGS density ( ρa) is obtainable for any liquid from equilibrium liquid vapor coexistence densities, as ρa = 2 ρm where ρm is the limiting T 0 mean density constant in the law of rectilinear diameters (LRD). We further report relevant discoveries for the square well model liquid. Within the margins of numerical uncertainty, as well width λ1, the amorphous ground state density ρRCP corresponds to a packing fraction 0.6366+0.0005 (Buffon’s constant 2/ π within uncertainty); the RCP ground state residual entropy per sphere S(0) ~ k B (Boltzmann constant) Moreover, for all square well fluids we observe that ρ a = ρRCP and the LRD mean density ρm = ρRCP /2. In conclusion, the current status of statistical theory of RCP will be extended and reviewed.
References Woodcock L. V., “Thermodynamic description of liquid state limits”, J. Phys. Chem. (B), 116 (12) 3734 3744 (2012).
23 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
E.3 (Oral)
SPHERE PACKINGS AND CRYSTAL CHEMISTRY
Michael O’Keeffe Department of Chemistry, Arizona State University, Tempe AZ 85287, U. S. A. Email: [email protected]
The underlying topology of many crystal structures can be expressed as a periodic graph. In most cases this graph has an embedding in which the shortest distances between vertices are equal and correspond to edges. They can be considered therefore as the graphs of packings of equal spheres with vertices at sphere centres and edges corresponding to sphere contacts. Edge transitive sphere packing graphs are of great importance in materials design and synthesis, and how and what we know about them will be reviewed. The zeolite problem is to find 6 coordinated sphere packings comprised of vertex sharing regular tetrahedra with additional constraints on the distances between tetrahedron centres. For these the optimum symmetry is a subgroup of the maximum symmetry of the graph.
24 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
F.1 (Invited Talk)
WHY DO SPHERES PREFER FCC PACKING WHEN SUBJECTED TO EXTERNAL FORCES?
Sascha Heitkam (1,2,#), Jochen Fröhlich (1) and Wiebke Drenckhan (2) 1. Institut für Strömungsmechanik, TU Dresden, Germany 2. Laboratoire de Physique des Solides, Université Paris Sud XI, Orsay, France # Email: Sascha.heitkam@tu dresden.de
Many physical systems consist of equal volume ”hard spheres”, such as micro bubbles, colloids, emulsions or granular media. Many of these sphere systems tend to sediment or cream under the influence of gravitational forces, leading to the formation of more or less ordered sphere packings. Systems which have the possibility to order typically form hexagonally close packed structures, which consist of layers of hexagonally arranged spheres, piled in different sequences. Even though many different layering configurations are possible (Figure 1), many researchers report a preference for fcc packing in different systems, the preference depending strongly on the packing dynamics and packing history.
Building on the results of numerical simulations conducted with an immersed boundary method [Kempe, 2012] and simple experiments, we show here that a simple mechanical argument is likely to be at the origin of such observations. Finite sized, non fcc stackings are mechanically unstable and transform under the weight or due to the impact of newly arriving compacting spheres [Heitkam, 2012]. We will show that a similar mechanism may be at work in creating an fcc preference in hard sphere systems under shear [Ackerson, 1988].
The importance of mechanical stability in both examples, ordering under gravity and under shear, puts in evidence the importance of the packing process in contrast to considerations of the final packing state only.
Figure 1: (left) Bubble crystal [van der Net, 2006] and (right) different hexagonally close packed configurations: fcc, hcp and rhcp.
References Ackerson et al. , Physical Review Letters, 61: 1031 1036, 1988 Heitkam et al. , Physical Review Letters, 108, 2012 Kempe et al. , Journal of Computational Physics, 231: 3663 3684, 2012 Van der Net et al., Soft Matter, 2:129 134, 2006
25 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
F.2 (Oral)
DENSEST COLUMNAR PACKINGS OF HARD SPHERES FROM SEQUENTIAL DEPOSITION
Ho Kei Chan Foams and Complex Systems, School of Physics, Trinity College Dublin, Ireland. Email: [email protected] / [email protected]
Identical hard spheres inside a cylinder exhibit a rich variety of densest columnar phases [Chan, 2011; Mughal, 2011; Mughal, 2012; Pickett, 2000] (Fig. 1), which can either be defect free, or consist of line defects [Mughal, 2011] that arise due to a structural periodicity set by the diameter ratio D between the cylinder and the spheres. In this talk, I will give an introduction to such densest phases, present a surprisingly simple method of sequential deposition [Chan, 2011] for their construction, and discuss the experimental relevance of such densest packings with nano , micro , colloidal and charged particles.
Figure 1: Densest packings at various values of the diameter ratio D, together with their corresponding unrolled surface patterns which clear demonstrate the existence of line defects. Each arrow indicates the structural periodicity of its corresponding surface pattern.
References Chan H. K., Phys. Rev. E 84 , 050302(R) (2011). Mughal A., Chan H. K. and Weaire D., Phys. Rev. Lett. 106 , 115704 (2011). Mughal et al., Phys. Rev. E 85 , 051305 (2012). Pickett G. T., Gross M. and Okuyama H., Phys. Rev. Lett. 85 , 3652 (2000).
26 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
F.3 (Oral)
PHYLLOTACTIC DESCRIPTION OF HARD SPHERE PACKING IN CYLINDRICAL CHANNELS
Adil Mughal (1,#), Ho Kei Chan (2), Aaron Meagher (2), Denis Weaire (2) and Stefan Hutzler (2) 1. Institute of Mathematics and Physics, Aberystwyth University, Penglais, Aberystwyth, Ceredigion, Wales, SY23 3BZ, United Kingdom 2. Foams and Complex Systems, School of Physics, Trinity College Dublin, Dublin 2, Ireland # Email: [email protected]
We study the optimal packing of hard spheres in an infinitely long cylinder. Our simulations have yielded dozens of periodic, mechanically stable, structures as the ratio of the cylinder (D) to sphere (d) diameter is varied [Mughal, 2011]. Up to D/d=2.715 the densest structures are composed entirely of spheres which are in contact with the cylinder. The density reaches a maximum at discrete values of D/d when a maximum number of contacts are established. These maximal contact packings are of the classic "phyllotactic" type, familiar in biology. However, between these points we observe another type of packing, termed line slip.
An analytic understanding of these rigid structures follows by recourse to a yet simpler problem: the packing of disks on a cylinder. We show that maximal contact packings correspond to the perfect wrapping of a honeycomb arrangement of disks around a cylindrical tube. While line slip packings are inhomogeneous deformations of the honeycomb lattice modified to wrap around the cylinder (and have fewer contacts per sphere).
Beyond D/d=2.715 the structures are more complex, since they incorporate internal spheres [Mughal, 2012], but an analysis in terms of contacts or constraints is still illuminating. We review some relevant experiments with hard spheres and small bubbles.
References Mughal A., Chan H. K., and Weaire D., Physical Review Letters, 106, 115704, 2011. Mughal et al., Physical Review E, 85, 051305, 2012.
27 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
F.4 (Oral)
HIGH DENSITY PACKINGS OF EQUAL CIRCLES IN RECTANGLES WITH VARIABLE ASPECT RATIO
E. Specht Institute of Experimental Physics, Otto von Guericke University of Magdeburg, 39106 Magdeburg, Germany Email: [email protected] / [email protected] magdeburg.de
Arranging a fixed number n of equal non overlapping circles in a rectangle with variable aspect ratio is a non standard packing problem. It arises if one has to decide how a certain number of circular items should be packed into a rectangular box when no assumption is made on the shape of the box. How must the box be designed to achieve the maximum packing density? This special problem was investigated by Lubachevsky and Graham [Discrete and Computational Geometry: The Goodman Pollack Festschrift, Springer 2003, pp. 633 650)], in 2003, where they classified record packings for n ≤ 213. However, their work lacks a precise treatment of the closure of observed vacancies as well as any numerical data of the best arrangements found.
In an article, recently published in Computers & Operations Research, a shorter notation for hexagonal dense packings in rectangular containers is introduced. Furthermore, a deterministic procedure is applied for the optimization of packings that differ from usual regular hexagonal patterns by one or more vacancies, without relying on simulation programs. A couple of improvements were found and numerical values are given for all packings in the extended range 1 ≤ n ≤ 500. Numerical results are also available at www.packomania.com/crc_var/
Keywords: Circle packing, Container design, Rectangular container, Variable aspect ratio, Hexagonal grid
2000 MSC: primary 52C17, secondary 05B40, 11H31
28 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
F.5 (Oral)
PACKING CONFINED HARD SPHERES DENSER WITH NEW PRISM PHASES
Erdal C. Oğuz (1,#), Matthieu Marechal (1), Fernando Ramiro Manzano (2), Elvira Bonet (3), Francisco J. Meseguer (3,4), René Messina (5) and Hartmut Löwen (1)
1. Institut für Theoretische Physik II, Heinrich Heine Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany 2. Nanoscience Laboratory, Dept. Physics, University of Trento, Via Sommarive 14, I 38050 Trento, Italy 3. Centro de Tecnologias Fisicas, Unidad Asociada ICMM/CSIC UPV, Universidad Politecnica de Valencia, Av. Los Naranjos s/n, 46022 Valencia, Spain 4. Instituto de Ciencia de Materiales de Madrid CSIC, 28049 Madrid, Spain 5. Institut de Chimie, Physique et Matériaux (ICPM), Université de Lorraine, 1 Bld Arago, 57078 Metz Cedex 3, France # Email: [email protected] duesseldorf.de
Close packing of hard spheres between two parallel hard plates yield a plenty of crystalline phases. We access the structure of the confined hard sphere crystals by theory, simulation, and experiment. For varying plate spacing H allowing up to four triangular monolayers, the known closest packed structures are confirmed by a numerical penalty method. We further predict new prism type structures which packs better than previously suggested ones: in the transition regime n□ → n , prism phases with rhombic and quadratic basis shape for n=2,3 are found to possess a higher packing fraction than the simple rhombic phase structures. Contrary to already known prism phases, the alternating prism like arrays of the new phases are only laterally shifted to each other in the plane parallel to confining plates. We confirm these new phases by Monte Carlo simulations at finite pressure and by real space data of confined sterically stabilized colloids.
29 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
G.1 (Oral)
A SIMPLE GRANOCENTRIC MODEL FOR PACKING OF POLYDISPERSE SPHERES
M. Clusel (#), E.I. Corwin, A.O.N Siemens and J. Brujic CNRS Universite Monptellier 2, France. # Email: maxime.clusel@univ montp2.fr
I will present and discuss a simple statistical model for the random packing of frictionless, originally introduced to find the link between polydispersity and packing structure. We simplify the problem by considering the “granocentric” point of view of a single particle in the bulk, thereby reducing random packing to the assembly of nearest neighbours, followed by a random choice of contacts among them. The model is based on only two parameters, the available solid angle around each particle and the ratio of contacts to neighbours, which are both directly obtainable from experiments or simulations. As a result, the model allows for the microscopic distributions of nearest neighbours and contacts, the local density fluctuations as well as the global density of the packing, given the size distribution of the particles. We find that this granocentric view captures the essential properties of the polydisperse emulsion packing. This model suggests a general principle of organisation for random packing and provides a statistical tool for quantifying the effect of the particle size distribution on the geometry of random packing in a variety of contexts of industrial relevance.
References Clusel et al. , Nature 460 (7255), 611 615, 2009. Corwin et al. , Soft Matter 6 (13), 2949 2959, 2010.
30 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
G.2 (Oral)
UNIVERSAL CORRELATIONS IN POLYDISPERSE FRICTIONLESS DISORDERED PACKINGS
Cathal B. O’Donovan (1,#), Eric I. Corwin (2) and Matthias E. Möbius (1) 1. School of Physics, Trinity College Dublin, Ireland 2. Department of Physics, University of Oregon, USA # Email: [email protected]
Wet foams and emulsions can be thought of as packings of frictionless spheres. The contact number distributions of these disordered packings are set by the particle size distribution [Clusel, 2009]. Using simulations of three dimensional packings made up of polydisperse frictionless spheres, we investigate how the size distribution affects correlations between sphere size and contact number at the random closed packing density. We find a linear relationship between the average contact number of a particle and its surface area. Surprisingly, this relation is independent of the size distribution of particles.
Using this result, we propose a simple model to predict the contact number distribution for a given polydispersity. The model yields excellent results for monodisperse, discrete and continuous size distributions.
Figure 1: Comparison between the contact number distribution P[z] and the predicted distribution from the model for different size distributions P[r]..
References Clusel et al. , Nature, 460:611 615, 2009.
31 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
G.3 (Oral)
MEAN FIELD APPROXIMATION OF POLYDISPERSE HARD SPHERE MIXTURES BY TRIDISPERSE SYSTEMS
Vitaliy Ogarko (#) and Stefan Luding Multi Scale Mechanics (MSM), CTW, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands. # Email: [email protected]
We study polydisperse mixtures of hard sphere fluids with extreme size ratios up to 100. Simulation results are compared with previously found analytical equations of state for the compressibility factor, and agreement is found with much better than 1% deviation in the fluid regime. When the density is further increased, excluded volume becomes important, but there is still a close relationship between many component mixtures and their binary, two component equivalents (which are defined on basis of the first three moments of the size distribution) [Ogarko, 2012]. However, equivalent binary mixtures show partial crystallization for relatively large size ratios. We show that an equivalent tridisperse system, which has the same first five moments of the size distribution as a given polydisperse one, do not show any signs of crystallization for the whole range of densities and agrees with the equation of state of the polydisperse mixture with at most 1% deviation. Analytical expressions for such equivalent systems are presented as well as the microstructural insight into equivalent jammed packings concerning rattlers. Furthermore, we determine the size ratios for which the liquid solid transition exhibits crystalline, amorphous or mixed system structure.
References V. Ogarko and S. Luding, J. Chem. Phys., 136:124508, 2012.
32 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
H.1 (Invited Talk)
THE SHAPE OF THE VORONOI CELLS INSIGHT INTO SPHERICAL BEAD PACKS
Gerd Schroeder Turk Institut für Theoretische Physik, Friedrich Alexander Universität, Erlangen Nürnberg, Germany. Email: Gerd.Schroeder [email protected] erlangen.de
In this talk, I will describe joint work on the analysis of local morphometric properties of disordered bead packs, and the insight it offers into the structural changes at RCP. First, I will report on the fundamental yet so far overlooked geometric property that disordered mono disperse spherical bead packs have significant local structural anisotropy manifest in the shape of the free space associated with each bead. These findings suggest an inherent geometrical reason why, in disordered packings, anisotropic shapes can fill space more efficiently than spheres [1].
Further, I will describe how this analysis can be generalised to a Minkowski analysis that is explicitly sensitive to the different types of local structure. The local structure of disordered jammed packings of monodisperse spheres without friction, generated by the Lubachevsky Stillinger algorithm, is studied for packing fractions above and below 64%. The structural similarity of the particle environments to fcc or hcp crystalline packings (local crystallinity) is quantified by order metrics based on rank four Minkowski tensors. We find a critical packing fraction φc ≈ 0.649, distinctly higher than previously reported values for the contested random close packing limit. At φc, the probability of finding local crystalline configurations first becomes finite and, for larger packing fractions, increases by several orders of magnitude. This provides quantitative evidence of an abrupt onset of local crystallinity at φ c. We demonstrate that the identification of local crystallinity by the frequently used local bond orientational order metric q6 produces false positives and thus conceals the abrupt onset of local crystallinity. Since the critical packing fraction is significantly above results from mean field analysis of the mechanical contacts for frictionless spheres, it is suggested that dynamic arrest due to isostaticity and the alleged geometric phase transition in the Edwards framework may be disconnected phenomena. [2].
References
[1] G.E. Schröder Turk, W. Mickel, M. Schröter, G.W. Delaney, M. Saadatfar, T.J. Senden, K. Mecke and T. Aste, "Disordered spherical bead packs are anisotropic", EPL 90, 34001 (2010)
[2] S.C. Kapfer, W. Mickel, K. Mecke, G.E. Schroeder Turk, "Jammed spheres: Minkowski tensors reveal onset of local crystallinity", Phys. Rev. E 85, 030301(R) (2012)
33 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
H.2 (Oral)
NON UNIFORMITIES IN THE PACKING PROPERTIES OF LARGE HEAPS OF GRANULAR MATTER
Nikola Topic (1,#), J. A. C. Gallas (1,2) and Thorsten Pöschel (1)
1. Institute for Multiscale Simulation, Friedrich Alexander Universität, Erlangen, Germany 2. Departamento de Física, Universidade Federal da Paraíba, João Pessoa, Brazil # Email: [email protected] erlangen.de
We report a numerical investigation of the structural properties of very large three dimensional heaps of granular material produced by ballistic deposition from extended circular dropping areas. Very large heaps are found to contain three new geometrical characteristics not observed before: they may have two external angles of repose, an internal angle of repose, and four distinct packing fraction (density) regions. Such characteristics are shown to be directly correlated with the size of the dropping zone. In addition, we also describe how noise during the deposition affects the final heap structure.
Figure 1: Left: Packing fraction for a 3D heap with five contours superimposed showing the growth history. The green line is the prediction of how the flat surface of the heap shrinks during initial phases of growth. The auxiliary straight line on the left heap boundary helps the visualization of the two angles of repose. The number of particles is N=107. Right: Schematic representation of a generic heap and its main characteristics: the angles of repose α, β and γh, where h is the height at which the angle is measured, and the four axially symmetric density zones A, B, C and D .
References W. M. Visscher and M. Bolsterli, Nature 239, 504 (1972). N. Topic, J. A. C. Gallas and T. Pöschel, submitted for publication.
34 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
I Public Lecture (Invited)
Paccar Theatre, Science Gallery, Tuesday, September 4, 19:00 19:50 http://sciencegallery.com/events/2012/09/experimental geometry experiments candies dice and colloids
EXPERIMENTAL GEOMETRY: EXPERIMENTS WI TH CANDIES, DICE AND COLLOIDS
Paul Chaikin Department of Physics, New York University, New York, USA. Email: [email protected] / [email protected]
Packing problems, how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. For equal spheres, Kepler conjectured in 1611 that the face centered cubic crystal has the highest possible packing fraction ϕ ~ 0.74, but the proof by Hales only came in 1998. It is also well known that the densest random (amorphous) packings have ϕ ~ 0.64. The density of packings in lattice and amorphous forms is intimately related to the existence of liquid and crystal phases and is responsible for the melting transition. We have studied the crystal liquid transition in spherical colloidal systems on earth and in microgravity in space and have confirmed this relation.
Non spherical particles are another matter. Ellipsoids can randomly pack more densely; up to ϕ ~ 0.68 to 0.71 for spheroids with an aspect ratio close to that of M&M’s Candies, and even approach ϕ ~ 0.75 for general ellipsoids. We have shown that the higher density relates directly to the fact that rotating an ellipsoid makes a difference while rotating a sphere doesn't (no surprise). The number of contacts per particle Z is ~10 for our M&M's as compared to Z ~ 6 for spheres. We have also found the ellipsoids can be packed in a crystalline array to a density, ϕ ~ 0.7707 which exceeds the highest previous packing. Tetrahedra are yet an active area with the densest packing unknown and different random, crystalline and quasicrystalline structures as candidates.
These results provide insights into granular materials, rigidity, jamming, and why amorphous glasses don't flow.
35 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
J.1 (Invited Talk)
AUTOREFERENTIAL ORDER: AN INFORMATION THEORETIC APPROACH TO ENCODE DISORDERED STRUCTURES
Tomaso Aste Department of Computer Science, University College London. School of Physical Sciences, University of Kent. Department of Applied Mathematics, The Australian National University. Email (until 1st Sep 2012): [email protected] Email (after 1st Sep 2012): [email protected]
The structure of complex non crystalline “amorphous” materials cannot be described as a defective form of order and it is not simply a random disposition of atoms in space. Real disordered structures show high degrees of organization that can propagate hierarchically through large portions of the material. Nonetheless, they do not present any periodic pattern and their structure is hard to encode in a compact form.
The key idea at the base of the present study is very simple: in absence of a pre definite template reference structure, we can use a part of the material as a reference structure for another part. The set of local structures from which the whole structure can be most efficiently encoded is the set of motifs associated to the original complex structure.
The methodology to identify these motifs is based on an information theoretic approach where the amount of information that a given sub part of the structure provides to describe the remaining part of the structure is quantified. The local motifs containing maximal relative information are the ‘encoding alphabet’. From the statistics of the occurrences, the fluctuations, the matching rules between the motifs one can efficiently describe of the entire structure with the shortest code length. To this purpose, information theory measures, such as mutual information, are used to quantify how much information a local portion of the structure carries about the whole system; the motifs are the most informative parts.
I will discuss applications of this method to data from x ray computed tomography (XCT) experimental packings and to structural datasets from large scale simulations.
36 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
J.2 (Oral)
GETTING RANDOM CLOSE PACKINGS OF CONVEX POLYHEDRA
Jean François Camenen
University of Bristol, U. K. Email: [email protected]
Works to study a perfectly random state of maximal solid fraction of granular packings concerned at first packings of spheres [Bernal, 1960; Macrae, 1961; Scott, 1969] and these first authors proposed calling this state Random Close Packings (RCP). As solid fraction is not sufficient to characterize a RCP state which has to integrate notion of threshold of packings rigidity [Torquato, 2000; Roux, 2000; Kansal, 2002], a definition of random state of maximal solid fraction was proposed by [Agnolin, 2007]: it is the state of stable equilibrium of homogeneous packings of rigid grains without friction in the contacts and for which the evolution towards crystalline state or towards segregation of mixtures remains unimportant. Here we focus on packings of convex polyhedra (pinacoids: eight faces, eight vertices, diameter d) Figure 1 left, and we want to check RCP definition for such systems. We model mono disperse packings obtained under gravity without friction by micro mechanical approach (DEM) Non Smooth Contact Dynamic [Moreau, 1994] implemented in the software platform LMGC90© [Dubois, 2003]. We test the model for various time steps (10−4 s and 5.10−4 s), sample sizes (1000 to 5000 particles) and boundary conditions (with side walls and periodic boundaries). We investigate packing micro structure according to the coordination number, solid fraction, stress and order. We obtained samples in equilibrium and homogeneous, noticing effects of the bottom wall on structure of the only first layer. We observed weak anisotropy of the normal contacts, no arrangement in translation and in particularly, only at very short range in orientation (r < d, Figure 1 right) verifying disorder in our packings. So, we get maximal solid fraction with a value of 0.761+/ 0.002 for random pinacoid packings much higher than spheres (~0.64) [Scott, 1969; Zhang, 2001; Roux, 2005].
Figure 1: (left) Typical 3D snapshots for mono sized packings of 1000 pinacoids. (right) Faces correlation function F(r) [Smith, 2010] for samples of 5000 pinacoids for time steps of 10 −4 s and 5.10 −4 s with side walls (WALL) and periodic boundaries conditions (PBC).
References Agnolin I. et al , Phys. Rev. E, 76:061302.1–061302.27, 2007. Bernal J. D. et al , Nature, 188:910–911, 1960. Dubois F. et al, Actes du sixième colloque national en calcul des structures CSMA AFM LMS, 1:111–118, 2003. Kansal A. R. et al, Phys. Rev. E, 66:041109, 2002. Macrae J. C. et al , British Journal of Applied Physics, 12(4):164–172, 1961. Moreau J. J., European J. Mech. A, 13:93–114, 1994. Roux J. N., Phys. Rev. E, 61:6802/6836, 2000. Roux J. N. et al , Bulletin des Laboratoires des Ponts et Chaussées, 2005. Scott et al , J. Appl. Phys., 2:863–866, 1969. Smith K. C. et al , Phys. Rev. E, 82:051304, 2010. Torquato S. et al , Physical Review Letters, 84:2064–2067, 2000. Zhang Z. P. et al , Powder Technology, 116:23–32, 2001.
37 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
J.3 (Oral)
A COMPLEX NETWORK APPROACH TO THE EQUILIBRIUM STATES IN GRANULAR PACKING
Roberto Arévalo (1,#), Luis Pugnaloni (2), Iker Zuriguel (3) and Diego Maza (3) 1. CNR SPIN, Dip. Scienze Fisiche, Università Federico II di Napoli, Italy 2. Dept. de Ingenieria Mecanica, Facultad Regional La Plata, Universidad Tecnologica Nacional, Argentina 3. Dept. Fisica y Matematica Aplicada, Facultad de Ciencias, Universidad de Navarra, Spain # Email: [email protected] / [email protected]
During (the past) years there have been several attempts to describe the structure of granular media. The so called force chains [Behringer, 1999] succeeded in highlighting the heterogeneous nature of stress distribution, but their applicability is limited due to the absence of an objective definition. Geometrical measurements, like the Voronoi tessellation[Aste, 2006], make use of information on particles' vicinity, and they have been useful in analyzing, for example, the amount of order in a system of particles. However, such analysis does not take into account the topology of the contact network and, thus, may not offer a complete description of a system of grains.
Recently, it has been shown [Pugnaloni, 2010] that the evolution of the packing fraction in a tapped system is non monotonous when the tapping amplitude is sufficiently high. Hence, states with equal packing fraction can be found at both sides of certain minimum density state.
In the present work we analyze the complex structure of the contact network developed in a granular tapped system. By means of molecular dynamics simulations we generate packings via a protocol which evolve like the experiments reported in [Pugnaloni, 2010]. We show that local geometrical analysis by itself fails to uncover the differences between apparently equivalent equilibrium states.
Instead, we use topological measurements on the contact network that allow a precise discrimination between states with equal number of particles and density. We find that the “motifs” of the network closed loops of contacts are particularly sensitive to characterize the contact structure and allow to discriminate between states with apparently equal geometrical properties.
References Aste et al., Europhysics Letters, 97: 24003, 2006. Behringer et al., Physica A 133: 1, 1999. Pugnaloni et al., Physical Review E 82: 050301(R), 2010.
38 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
J.4 (Oral)
SIZE TOPOLOGY RELATIONS: DISORDER IN TILINGS AND PACKINGS
Sascha Hilgenfeldt Mechanical Science and Engineering, University of Illinois at Urbana Champaign, U. S. A. Email: [email protected]
Many characteristics of structure and morphology are shared by biological tissues, foams, and a large class of other materials characterized by tilings and packings. What can we learn about the physics and function of these systems from such properties, either universal or specific? Which features are a consequence of mathematical necessity, of physical interactions, or of biological processes?
We explore these questions with disordered structures of epithelial tissues as a starting point. We find that quantitative modeling is possible with only minimal reference to biological processes, or indeed long range spatial correlations. In two dimensions, cell neighbour relations in the disordered epithelium of the Drosophila wing are captured by a statistical mean field approach derived from a local model, successful for all morphogenetic stages. The same approach reveals strong relations between moments of cell size distributions and topology distributions, which prove applicable to a much larger class of systems both living and inanimate, cf. Fig.1. As the approach constructs tilings from 2D packings, it also provides insight into disordered packings and their transition from order to disorder. Long standing conjectures in tiling and packing systems can now be demonstrated analytically (Miklius and Hilgenfeldt 2012). In three dimensions, this local model allows for the separation of size disorder and positional disorder, leading to separate analytical predictions for the size topology statistics of monodisperse and polydisperse packings in 3D (Newhall et al. 2012). Figure 2 shows that this distinction holds for a wide variety of packing and tiling systems.
Figure 2: Generalized Lewis Law: In three dimensional packings, the average size of local volumes with a given number of neighbors follows distinct laws for monodisperse packings (positional disorder dominates) Figure 1: Relation between coefficients of variation and polydisperse packings (size disorder dominates) with of cell area (abscissa) and of topology (ordinate) a range of polydispersities. The results are very similar for for various two dimensional cellular systems. The strongly deformed packings approaching foam like tilings solid red line is an analytical prediction from the (Newhall et al. 2012). pr esent model (Miklius and Hilgenfeldt 2012). References Miklius, M., and S. Hilgenfeldt. Phys. Rev. Lett. 108 , 015502 (2012). Newhall, K., L. L. Pontani, I. Jorjadze, S. Hilgenfeldt, and J. Brujic, Phys. Rev. Lett. 108 , 268001 (2012).
39 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
K.1 (Oral) TOMOGRAPHY OF MONODISPERSE LIQUID FOAMS
A. J. Meagher (1,#), M. Mukherjee (2), D. Weaire (1), S. Hutzler (2), J. Banhart (2) and F. Garcia Moreno (2) 1. School of Physics, Trinity College Dublin, Dublin 2, Ireland 2. Helmholtz Zentrum Berlin, Hahn–Meitner–Platz, 14109 Berlin, Germany # Email: [email protected]
The unique ordering behaviour and modelling potential of monodisperse microfoam has led to their continued study for over 60 years [Bragg, 1947]. However, in this pursuit, the limits of optics have frustrated their complete characterisation [van der Net, 2007]. With the advent of low energy X ray tomography we now possess the experimental technique required to fully investigate their internal structure and further propel their application as a model system for a wide variety of physical systems [Gouldstone, 2001].
Using a CT device, we constructed the first successful three dimensional imaging of a monodisperse liquid microfoam produced with ordinary surfactant solution [Meagher, 2011]. The previously reported surface crystallisation of such foams was seen to propagate several layers into the foam core, resulting in the complete crystallisation of small samples (~8000 bubbles) (see Fig. 1). In such crystals, many defects such as interstices, vacancies and grain boundaries were seen to form due to the nature of the container geometry. In larger samples (~15,000 bubbles) complete sample crystallisation did not occur. Instead, it was found that the bulk was arranged in a random packing of spheres, with the radial distribution function of a Bernal structure. This is the first experimental evidence that such a structure occurs in foam samples. Based upon these findings, we have conducted initial experiments investigating how the samples evolve with time. Using visualisation techniques based upon the bond orientational order parameter, we have found that large samples tend to evolve to an ordered state over time, with regions of hexagonal order along the boundary propagating into the disordered bulk.
Figure 1: X ray topographic reconstruction of an ordered sample of 8000 monodisperse microbubbles with average diameter 800 m. The bubbles are seen to spontaneously order, forming the ABC packing of spheres associated with FCC crystallisation.
References Bragg L. and Nye, J. F., Proc. R. Soc. Lond. A, 190 (1023), 474 481 Gouldstone et al. , Nature 411, 656 (2001). Meagher et al. Soft Matter, 7, 9881 9885 (2011). Van der Net et al. , Coll. Surf. A, 309, 159 176 (2007).
40 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
K.2 (Oral)
APPLICATIONS OF X RAY IMAGING TECHNOLOGY IN GRANULAR PHYSICS
Yujie Wang
Physics Department, Shanghai Jiao Tong University, Shanghai, China Email: [email protected]
It’s important to understand both static and dynamic properties of a granular system. Studying granular systems with x ray imaging technology, including x ray computed tomography (CT) and ultrafast x ray projection imaging, has great superiority. Due to the penetrating properties of x ray, internal structures of a granular system could be obtained. Using x ray CT technology, we studied packing problems with various granular systems, such as mono dispersed hard spheres, wet spheres, rods, poly dispersed foams, etc. At the same time, ultrafast x ray phase contrast imaging technology based on synchrotron radiation provides a projective realization of evolving systems, which is one of the few experimental methods that can probe dynamic properties of granular systems. Using the above technology, we implement dynamic projective tracking of 3D granular gas, granular pipe flow, and granular system under shaking. With these dynamic systems, we studied energy partition problems in granular systems, and analyzed concepts such as effective temperatures in granular systems, dynamic heterogeneity, and self organized criticality in granular jamming transition, etc. These experimental works will contribute to revealing some important properties of granular systems.
41 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
P.1 (Poster)
AN EXPERIMENTAL REALIZATION OF THE WEAIRE PHELAN STRUCTURE IN MONODISPERSE LIQUID FOAM
Ruggero Gabbrielli (1,2), Aaron J. Meagher (1,#), Denis Weaire (1), Kenneth A. Brakke (3) and Stefan Hutzler (1) 1. School of Physics, Trinity College Dublin, Ireland 2. Department of Physics, University of Trento, Italy 3. Department of Mathematical Sciences, Susquehanna University, U. S. A. # Email: [email protected]
The Weaire Phelan (WP) structure is the lowest energy structure known of an ideal monodisperse foam in the dry limit. Up to now it has not been realised in the laboratory. Instead Lord Kelvin’s 1887 structure, which it supplanted in 1994, has repeatedly been found in attempts to produce an ordered structure. This paradox is attributable to the flat walls of the containers used, with which the Kelvin structure is more compatible. Accordingly, we have fabricated a patterned mould whose faceted walls conform to the WP geometry, and thereby succeeded in inducing the formation of perfect crystals of the WP structure. Foam samples consisted of approximately 1,500 bubbles. Vibrations favoured crystallization.
42 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
P.2 (Poster)
SMARTIES AND RUGBY BALLS
Denis Weaire (1,#) and Adil Mughal (2) 1. School of Physics, Trinity College Dublin, Dublin 2, Ireland 2. Institute of Mathematics and Physics, Aberystwyth University, Penglais, Aberystwyth, Ceredigion, Wales, SY23 3BZ, United Kingdom # Email: [email protected]
The packing of oblate and prolate spheroids present interesting problems for theory and simulation, addressed by Chaikin and collaborators in recent years. We revisit the problem to discuss what is understood and what is not, and how simulations may be best performed [Mughal, to be published], both in bulk and in cylinders [Research supported by Science Foundation Ireland].
References Mughal A. and Weaire D., to be published Meagher et al. , to be published.
43 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
P.3 (Poster)
AN INVESTIGATION INTO CEREAL GRAIN PACKING
Jacek Wychowaniec (#), Adil Mughal, Alan Gay and Irene Griffiths Institute of Mathematics and Physics, Aberystwyth University, Penglais, Aberystwyth, Ceredigion, Wales, SY23 3BZ, United Kingdom # Email: [email protected]
Cereal products are one of the most important staple foods for both humans and domesticated livestock. The cultivation and transport of cereal grain is an enormous global industry. Due to the economies of scale involved, even small improvements in the efficient packaging and transport of grain can translate into considerable financial savings. Indeed, the sole criterion used in agriculture for the quality of cereal product is the grain density (i.e. mass of grain per unit volume) also known as the Hectolitre mass (HTM).
Using simple imaging techniques we characterize a range of common oat products. We show that individual grains can be approximated as hard ellipsoidal particles and measure the lengths of their semi minor & semi major axes. We find that for each product the values of the semi major lengths are well described by a bidisperse distribution. Using a simple tapping/shaking experiment we are able to systematically increase the packing density of all the grain samples. Our protocol is to pour the grain into a tubular container; this forms an initial random close packed state. We then shake the sample violently for a fixed amount of time; then shake the sample for the same amount of time but slightly less vigorously, and so on until a maximum packing density is achieved. In this final state we observe a qualitative difference in the alignment of ellipsoidal grains as compared to the initial state.
These preliminary findings are of interest to the packing community, which has in recent years been concerned with the random packing of non spherical objects, and also to the agriculturalists for whom packing density is an important measure of quality.
44 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
P.4 (Poster)
BUILDING THE PYRAMIDS: PERFECT BUBBLE CRYSTALS
David McAllister, Aaron Meagher, Stefan Hutzler (#) and Denis Weaire School of Physics, Trinity College Dublin, Ireland. # Email: [email protected]
The spontaneous crystallization of monodisperse microfoams first studied by Bragg has been the subject of intense study for over 60 years. Here we report on a novel technique, involving the use of pyramidal containers for the production of perfect single crystals independent of the bubble size employed. Through careful selection of the vertex angle of three and four sided pyramids, we have successfully provoked the crystallization of monodisperse foams into fcc, bcc and sc configurations. Defect free fcc crystals were made, while the production of bcc crystals were limited by bubble size. Sc crystals were limited in size by mechanical instability. The production of a coherent grain boundary within a foam crystal and the formation of ordered bidisperse foams were also studied.
45 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
2. List of Participants
2(a) Invited speakers
Title Name Affiliation(s) & Email Abstract title(s)
Trinity College Dublin (Ireland) A.1 PACKING PURSUITS (INVITED) Prof. Denis Weaire [email protected] P.2 SMARTIES AND RUGBY BALLS (POSTER)
Gerd Schroeder Friedrich Alexander Universität (Germany) H.1 THE SHAPE OF THE VORONOI CELLS INSIGHT INTO Dr. Gerd.Schroeder [email protected] Turk erlangen.de SPHERICAL BEAD PACKS University College London (UK) Prof. John Finney E.1 RANDOM PACKING BEFORE THE ARK [email protected]
University of Manchester (UK) Prof. Les Woodcock E.2 - THERMODYNAMIC STATUS OF RANDOM CLOSE PACKING [email protected]
Utrecht University (The Netherlands) B.1 DENSE REGULAR PACKINGS OF IRREGULAR NONCONVEX Prof. Marjolein Dijkstra [email protected] PARTICLES
New York University (USA) I EXPERIMENTAL GEOMETRY: EXPERIMENTS WITH CANDIES, Prof. Paul Chaikin DICE AND COLLOIDS (PUBLIC LECTURE) [email protected] / [email protected] C.1 - PRECISELY CYCLIC SAND (INVITED) Institut für Strömungsmechanik (Germany) F.1 WHY DO SPHERES PREFER FCC PACKING WHEN SUBJECTED Mr. Sascha Heitkam & Université Paris Sud XI, Orsay (France) Sascha.heitkam@tu dresden.de TO EXTERNAL FORCES? University College London (UK) J.1 AUTOREFERENTIAL ORDER: AN INFORMATION THEORETIC Dr. Tomaso Aste [email protected] APPROACH TO ENCODE DISORDERED STRUCTURES
2(b) Other presenters
Title Name Affiliation(s) & Email Abstract title(s)
Trinity College Dublin (Ireland) K.1 TOMOGRAPHY OF MONODISPERSE LIQUID FOAMS. Mr. Aaron Meagher P.1 AN EXPERIMENTAL REALIZATION OF THE WEAIRE PHELAN [email protected] STRUCTURE IN MONODISPERSE LIQUID FOAM (POSTER)
Aberystwyth University (UK) F.3 PHYLLOTACTIC DESCRIPTION OF HARD SPHERE PACKING IN Dr. Adil Mughal [email protected] CYLINDRICAL CHANNELS
Universidad de Sevilla (Spain) A PLANAR PARTITIONING PROBLEM: DIVIDING A PLANAR DISK INTO Dr. Antonio Cañete [email protected] REGIONS OF PRESCRIBED AREAS
Cathal Trinity College Dublin (Ireland) G.2 UNIVERSAL CORRELATIONS IN POLYDISPERSE FRICTIONLESS Mr. O’Donovan [email protected] DISORDERED PACKINGS Otto von Guericke University of Magdeburg (Germany) F.4 HIGH DENSITY PACKINGS OF EQUAL CIRCLES IN RECTANGLES Prof. Eckard Specht [email protected] WITH VARIABLE ASPECT RATIO [email protected] magdeburg.de Aberystwyth University (UK) Dr. Edwin Flikkema D.2 FROM CLUSTERS OF PARTICLES TO 2D BUBBLE CLUSTERS [email protected]
Heinrich Heine Universität Düsseldorf F.5 PACKING CONFINED HARD SPHERES DENSER WITH NEW PRISM Mr. Erdal C Oğuz (Germany) [email protected] duesseldorf.de PHASES University of Liège (Belgium) B.2 STRONG INTERLOCKING OF NON CONVEX PARTICLES IN Dr. François Ludewig [email protected] RANDOM PACKING
Otto von Guericke University (Germany) C.4 PATTERN FORMATION IN CONTINUOUSLY AGITATED TWO Mr. Frank Rietz [email protected] DIMENSIONAL PACKINGS
Trinity College Dublin (Ireland) F.2 DENSEST COLUMNAR PACKINGS OF HARD SPHERES FROM Dr. Ho Kei Chan [email protected] [email protected] SEQUENTIAL DEPOSITION Jacek Aberystwyth University (UK) Mr. P.3 AN INVESTIGATION INTO CEREAL GRAIN PACKING (POSTER) Wychowaniec [email protected]
46 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
Jean François University of Bristol (UK) Dr. J.2 GETTING RANDOM CLOSE PACKINGS OF CONVEX POLYHEDRA Camenen [email protected] Coventry University (UK) & Johannes Dr. Martin Weigel Gutenberg Universität Mainz (Germany) A.4 REGULAR PACKINGS ON PERIODIC LATTICES [email protected] Universite Monptellier (France) G.1 A SIMPLE GRANOCENTRIC MODEL FOR PACKING OF Dr. Maxime Clusel maxime.clusel@univ montp2.fr POLYDISPERSE SPHERES
University of Michigan (USA) A.2 SELF ASSEMBLY AND PACKING OF HARD POLYHEDRA INTO Dr. Michael Engel [email protected] COMPLEX STRUCTURES
Arizona State University (USA) Prof. Michael O’Keeffe E.3 SPHERE PACKINGS AND CRYSTAL CHEMISTRY [email protected]
Institut de Physique et Chimie des C.3 DILATANCY IN GRANULAR MEDIA UNDER SHEAR: A ROUTE TO Prof. Nick Rivier Matériaux de Strasbourg (France) [email protected] strasbg.fr CLOSER PACKING? Friedrich Alexander Universität / H.2 NON UNIFORMITIES IN THE PACKING PROPERTIES OF LARGE Mr. Nikola Topic Universität Erlangen Nürnberg (Germany) [email protected] erlangen.de HEAPS OF GRANULAR MATTER Universidad Politecnica de Madrid (Spain) B.4 ENTROPY DRIVEN CRYSTALLIZATION IN DENSE SYSTEMS OF Prof. Nikos Karayiannis [email protected] ATHERMAL CHAIN MOLECULES
Pierre M. UPMC (France) B.3 RANDOM PACKINGS OF SPIKY PARTICLES: GEOMETRY AND Dr. Adler [email protected] TRANSPORT PROPERTIES
Università Federico II di Napoli (Italy) J.3 A COMPLEX NETWORK APPROACH TO THE EQUILIBRIUM STATES Dr. Roberto Arévalo [email protected] [email protected] IN GRANULAR PACKING Sascha University of Illinois at Urbana Champaign J.4 SIZE TOPOLOGY RELATIONS: DISORDER IN TILINGS AND Prof. Hilgenfeldt (USA) [email protected] PACKINGS
Aberystwyth University (UK) D.1 HEXAGONAL OR CIRCULAR? PACKING A FINITE COLLECTION OF Prof. Simon Cox [email protected] DEFORMABLE OBJECTS
Trinity College Dublin (Ireland) D.3 CRYSTALLINE POLYHEDRAL FOAM COLUMNS Prof. Stefan Hutzler P.4 BUILDING THE PYRAMIDS: PERFECT BUBBLE CRYSTALS [email protected] (POSTER) Friedrich Alexander Universität / Prof. Thorsten Poeschel Universität Erlangen Nürnberg (Germany) C.2 FRACTAL SUBSTRUCTURE OF A NANOPOWER [email protected] erlangen.de University of Twente (The Netherlands), G.3 MEAN FIELD APPROXIMATION OF POLYDISPERSE HARD SPHERE Mr. Vitaliy Ogarko [email protected] MIXTURES BY TRIDISPERSE SYSTEMS
Princeton University (USA) Dr. Yoav Kallus A.3 WORST PACKING SHAPES [email protected]
Shanghai Jiao Tong University (China) K.2 APPLICATIONS OF X RAY IMAGING TECHNOLOGY IN GRANULAR Prof. Yujie Wang [email protected] PHYSICS
2(c) Other attendants
Title Name Affiliation(s) & Email
University of Liège (Belgium) Mr. Erico Opsomer [email protected]
Trinity College Dublin (Ireland) Mr. Gavin Ryan [email protected]
Trinity College Dublin (Ireland) Prof. Matthias Möbius [email protected]
University of Manchester (UK) Prof. Michael A. Moore [email protected]
Trinity College Dublin (Ireland) Mr. Michael Sexton [email protected]
47 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
University of Kent (UK) Mr. Paul Butler [email protected]
University College Dublin (Ireland) Prof. Peter Lynch [email protected]
Trinity College Dublin (Ireland) Mr. Robert Murtagh [email protected]
Trinity College Dublin (Ireland) Mr. Steven Tobin [email protected]
VTT Technical Research Centre (Finland) Dr. Tuomo Hjelt [email protected]
48 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
3. Web Access at Trinity College Dublin
Codes for wireless access will be distributed during registration. Please use the following web addresses for accessing the web: http://isservices.tcd.ie/network/wireless_guest_win7.php http://isservices.tcd.ie/network/wireless_guest_mac.php http://isservices.tcd.ie/network/wireless_guest_vista.php http://isservices.tcd.ie/network/wireless_guest_xp.php
4. Map of Dublin City Centre, and how to get there
The best way to reach the city centre from the airport is to take an Aircoach outside the arrivals hall. The coach will drop you to the city centre near Trinity College Dublin. Please click on the following link http://www.aircoach.ie/ for further information. The following is a map of Dublin City Centre which indicates the location of Trinity College Dublin as well as of Messrs Maguire (at Burgh Quay) for the Workshop dinner.
49 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012 5. Map of Trinity College Dublin
Public Lecture & Pre Lecture Reception : Science Gallery
Workshop venue: Fitzgerald Building (Fitzgerald Library & Schrodinger Lecture Theatre)
Lunch : Buttery Food Court
50 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012 6. Accommodation near Trinity College Dublin
The following is a list of hotels around the perimeter or in close proximity to TCD. Please book your preferred hotel via the hotel websites below or via other websites such as: http://www.hotels.com/ http://www.expedia.ie/ , http://www.dublintourist.com/directory/accommodation/hotels/city_centre/trinity_college_area/
Bushwell Hotel O’Callaghan's Davenport Hotel http://www.buswells.ie http://www.davenporthotel.ie/
Trinity Lodge Trinity Capital Hotel http://www.trinitylodge.com/ http://www.trinitycapitalhotel.com/
Kildare Street Hotel O’Callaghan's Mont Clare Hotel http://www.kildarestreethoteldublin.com/ http://www.montclarehotel.ie/
7. Things to do in Dublin
7(a) One Day in Dublin You have a day to spare in Dublin you`d like some Irish food , some history and some sightseeing then we`d recommend this self guided tour. Start your day with a breakfast at Bewleys, see some sights and finish the day with some traditional Irish food at Gallaghers Boxty House. You`ll experience an Irish breakfast , hear about some of our Irish history / heroes and finish the day with a traditional meal or alternatively an Italian at Milanos which is suitable for adults and kids alike.
1. Start the day early with breakfast at Bewleys . http://bewleys.com/bewleys grafton street cafe/our menus/breakfast
2. Follow this with a sightseeing tour of Dublin to get your bearings. http://dublincitytours.com/
3. Stop off at Dublinia to experience medieval Dublin life and the world of Vikings http://www.dublinia.ie/
4. Walk up from Christchurch to the Guinness Storehouse a popular tour of the brewery finished off by a pint of Guinness with great views from the Gravity bar . http://www.guinness storehouse.com/en/Index.aspx
5. Get a Red line Luas to Suir Road on the Luas line to Kilmainham Gaol for a tour of the famous jail that housed prisoners which fought for Irish Independence. http://www.heritageireland.ie/en/Dublin/KilmainhamGaol/
6. Finish off your day with a traditional Irish meal at Gallagher's Boxty house or if the kids fancy a pizza try out Milano in Dawson Street. http://www.boxtyhouse.ie/
51 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
7(b) Dublin City Tour
http://dublincitytours.com/
VITAL STATS Prices From: 16.00 EUR Duration: 1.5 Hours Runs: Varied Run Times
TOUR DETAILS One Ticket Two Routes + Exclusive Offers! This fun and friendly 90 minute tour is complete with live commentary by professionally trained local guides.
Tours depart every 6 to 15 minutes from O Connell St Upper throughout the day and stops along the tour route include Trinity College, the Guinness Storehouse, Dublin Castle, St Patrick's Cathedral, Kilmainham Gaol and the Old Jameson Distillery. Discounts off admission are available on many of these attractions with the Gray Line Dublin Tour ticket.
Tour tickets are also valid on the Dublin City Sightseeing Tour and your ticket will allow you a great 10% discount off your next City Sightseeing Tour in any of 60 cities worldwide!
Some places of interest along the tour route include:
Dublinia One of the most popular visits in the city, the exhibition portrays life in medieval Dublin 1170 to the Reformation circa 1540.
Guinness Storehouse With bars, a gallery and events it's the home, heart and soul of Guinness. Enjoy your complimentary pint with views of Dublin.
Old Jameson Distillery With origins dating back to 1870 today's visitor centre at the OJD introduces visitors to the taste and history of John Jameson's Irish whiskey.
Dublin Castle Home to the impressive Chester Beatty collection.
Phoenix Park Largest enclosed park in Europe and home to Dublin Zoo.
National Gallery, Ireland Home of the national collection of Irish art and works by European master painters.
52 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
7(c) Viking Splash Tour
http://www.vikingsplash.com/
Tours depart from St. Stephen's Green North. Join us for a fun and completely unique tour of Dublin by land and water in our reconditioned World War II vintage amphibious militaryvehicles called "Ducks". Our costumed and colourful Viking Tour Captains will tell you all about the most exciting sights in Dublin: how the Vikings first settled the City over 1000 years ago and how Dublin has become a thriving, cosmopolitan European city. Finally, you¡¦ll experience a real thrill as our Tour Captain drives the Duck into the waters of the historic Grand Canal Basin for the water portion of the tour. You may even be asked to give a Viking Splash Tours roar at passers by! Viking Splash Tours is a family tour suitable for all ages, young and old. However, we do not have life jackets for children under three years old and they therefore cannot come on the water portion of the tour. If you would like to bring a very young child on the tour you must be prepared to come off the tour and wait on the quayside for the water portion (approx. 20 minutes) and rejoin the tour afterwards. In this instance there is no charge for the child, however the full ticket price does apply to the adult.
There are 28 seats on every "Duck". Seating is on a first come, first served basis. We board each tour 10 minutes before the official departure time. There are eight seats at the back of every "duck" that are not under the roof. In the case of rain the people who purchased the last eight tickets for the tour will be obliged to sit in those seats and will be notified beforepurchasing the tickets. We provide rain ponchos and umbrellas on all ducks for these seats. You do not get wet on the tour so a change of clothes is not necessary. We do recommend a jacket as it can get chilly on the water and the "Ducks" are not heated. Purchase tickets at the departure point.
53 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
7(d) Cultural Days Out
Dalkey Castle & Heritage Centre
http://www.dalkeycastle.com/
Dalkey is a stylish and historic little village situated at the southern end of Dublin bay. The Dalkey Castle and Heritage centre fits in well with the area. It has a 15th century townhouse, a 10th century church and graveyard, an art gallery and a new writers gallery. There are regular tours of the castle which include a Living History experience and costumed medieval archers giving a lively historical background to the castle and area. Scaled models and information panels with text written by local Tony Award winner, Hugh Leonard, vividly illustrate the history of the area. The rich literary history of the area is enhanced by the fact that James Joyce set Chapter Two of Ulysses in Dalkey. A short Introductory Tour is included in the admission price. You can view a video of the archaeology of the area, presented by Archaeologist, Chris Corlett.
Families can: explore Goat Castle with its murder hole. view models of Medieval Dalkey, the Atmospheric and Funicular railways and the trams. visit the 10th century St Begnet`s Church & Graveyard. enjoy Heritage Trails & Historical Walks in Dalkey, which begin at the Heritage Centre. enjoy Living History Live Performance every half hour Actors in medieval costume will bring the fascinating history of the castle to life, where you can hear about customs & other stories. enjoy food at local restaurants in Dalkey village.
Stroll through the centuries ...with a visit to Dalkey Castle & Heritage Centre and one of their guided walking tours! Opens Daily: but times vary so check their web site for more detail Price : Varies depending on adult or children How to get there : 10 mins walk from Dalkey Dart station
Dublin Castle (Dame St., Dublin 2)
http://www.dublincastle.ie/
54 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
Dublin Castle for seven centuries was a symbol of English rule since the Anglo Normans built a fortress. All that remains of the original structure are the butt of the Norman Powder Tower and the Record Tower. The tour of the castle gives you a feel for the high life of old royalty and political elite. Outside the castle has an older history. In 830 AD some 60 warships sailed up the Liffey and set up home in Dublin. The Irish expelled the Vikings and they relocated just west of the castle to set up a town called Dylflinn (later Dubh Linn) which is where the name Dublin derived its name. This area is the circular garden just in front of the Chester Beatty library.
What can you see at the Castle : The Undercroft is sited at lower ground floor level in the Lower Castle Yard, immediately beside The Castle Vaults Bistro and Castle Gift Shop. The city walls join the Castle at this point. Here, the archway allowed small feeder boats to land provisions at the postern gate, from larger boats moored on the Liffey. The double archway and postern gate are still visible. Also on view here is the Viking defence bank, within the butt of the Norman Powder Tower. The original Tower was five stories high the top storey being occupied by the Lord Deputy. The Chapel Royal is a gothic revival building designed by Francis Johnston. It is famous for its vaulting, its particularly fine plaster decoration and carved oaks and galleries. Of particular interest are the coats of arms of the Justiciars, Lord Deputies and Lord Lieutenants from the first, St Hugh de Lacy (1172), which was two years after the Norman invasion, to the last, FitzAlan (1922), which, remarkably, occupies the last available space. The State Apartments dominate the south range of the Great Courtyard. They were built as the residential and public quarters of the Viceregal Court. An account of Viceregal Court life is given in Chapter 15 of the Dublin Castle History. Today the Apartments are the venue for Ireland`s Presidencies of the European Union, Presidential inaugurations and prestigious functions. St Patricks Hall : This hall with its banners of the now defunct Knights of St Patrick has some famous ceiling paintings symbolizing the relationship between Britain and Ireland. Throne Room: Built in 1740 this room contains a throne which was said to have been presented by William of Orange after the victory of the Battle of the Boyne
While at Dublin Castle why not visit : 1. The Garda Museum 2. Chester Beatty Library
Interesting fact(s) about Dublin Castle : 1. Robert Emmet : A leader of the abortive 1803 rebellion and was a heroic champion of Irish Liberty. His plan to capture Dublin Castle as a signal for the country to rise up against the Act of Union failed and he was caught and publicly hanged. His rousing patriotic speech from the dock before he died is said to have inspired many an Irish freedom fighter.
Dublin's City Hall (Dame St., Dublin 2)
http://www.dublincity.ie/RecreationandCulture/MuseumsGalleriesandTheatres/CityHall/Pages/city_hall _hub.aspx
55 International Workshop on PACKING PROBLEMS School of Physics, Trinity College Dublin, 2 – 5 September, 2012
City Hall was designed by Thomas Cooley as the Royal Exchange between 1769 and 1779. It is one of Dublin`s finest neo Classical buildings and the City Hall exhibition is a multimedia journey through the centuries capturing a thousand years of Dublin's history. This exhibition brings to life the changes in the city tracing the evolution of the city from 1170 to the present day with particular emphasis on the development of the civic government. The story is told through the display of Civic Regalia, including the Great City Sword, the Great Mace, the Lord Mayor's chain and city treasures, which are supported by computer interactives, archive films, models and costumes.
Opens Daily: but times vary so check their web site for more detail Price : Varies depending on adult or children How to get there: 5 mins walk from Tara Street station
Trinity College & Book of Kells (College St., Dublin 2)
http://www.tcd.ie/ http://www.tcd.ie/Library/bookofkells/book of kells/ Founded in 1592 Trinity College is Dublin`s oldest college. Among its many famous students were Jonathon Swift, Osca Wilde, Oliver Goldsmith, Samuel Beckett and Bram Stoker. Originally a Protestant only college, Catholics were forbidden to join unless they accepted the Protestant faith. These restrictions weren`t lifted until 1970. The college covers 40 acres and lies in the city centre on the south side of the river just at the end of Grafton Street. It is home to one of the most famous books in the world the Book of Kells Ireland`s medieval illuminated manuscript thought to be the work of some somes from Iona who fled to Kells in AD 806 after a Viking raid. The book was moved to Trinity college in the 17th century.
What can you see at Trinity? 1. Old Library and Book of Kells Inside the grand old Library there are over 200,000 books. The most famous of these being the Book of Kells the illuminated manuscript contains 4 gospels written in Latin around AD800 and is lavishly decorated with elaborate patterns and mythical animals, influenced by the hand wrought metalwork traditions of that period. Described by a 13th century chronicler as "a work not of men but of angels". A must see. 2. Burke and Goldsmith statues Guarding the Main entrance are two statues of political writer Edmund Burke (1868) and playwright Oliver Goldsmith (1867) 3. Chapel (1798) The first university chapel in southern Ireland to accept all denominations. 4. Campanile 98ft bell tower built in 1853 by Charles Lanyon the architect of Queen`s University of Belfast. 5. Museum Building Check out the Geology museum for meteorites, fossils and early amphibians. Dates back to mid 19th century and on entering you will see two skeletons of giant Irish deer. The famous inventor of the humane hangman's drop was a professor here. 6. Sphere within a Sphere was given to the college by sculptor Arnaldo Pomodoro. Situated outside the Berkeley Library.
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