19 research outputs found
Soft Sphere Packings at Finite Pressure but Unstable to Shear
When are athermal soft sphere packings jammed ? Any experimentally relevant
definition must at the very least require a jammed packing to resist shear. We
demonstrate that widely used (numerical) protocols in which particles are
compressed together, can and do produce packings which are unstable to shear -
and that the probability of generating such packings reaches one near jamming.
We introduce a new protocol that, by allowing the system to explore different
box shapes as it equilibrates, generates truly jammed packings with strictly
positive shear moduli G. For these packings, the scaling of the average of G is
consistent with earlier results, while the probability distribution P(G)
exhibits novel and rich scalingComment: 5 pages, 6 figures. Resubmitted to Physical Review Letters after a
few change
Juxtapositions Rigides de Cercles et de Sphères. Partie II: Juxtapositions Infinites de Mouvement Fini
Une juxtaposition P de cercles dans le plan est dite n-stable pour n = 1,2, . . . si tout ensemble de n cercles est tenu fixe par les autres. Pest destabilité finie si elle est n-stable pour tou t n = 1,2, . . . Parmi les 31 familles de juxtapositions régulières connexes de cercles dans le plan que I'on a classifiées, certaines sont de stabilité finie, d'autres non. Dans 3 des cas de familles de juxtapositions qui ne sont pas de stabilité finie, il apparaït que la plus petite valeur de n
pour laquelle elles ne sont pas n-stables est arbitrairement grande, et dépend d'un paramètre de la familleA packing P of circles in the plane is called n-stable, for n = 1,2… if every set of n circles is held fixed by the rest. P is called finitely stable if it is n-stable for every n = 1, 2,. . . For each of the 31 families of regular connected circle packings in the plane we classify which are finitely stable and which are not. For 3 of the cases when the families of packings are not finitely stable, it turns out that the smallest n for which they are not n-stable gets arbitrarily large,
depending on a parameter of the family.Peer Reviewe
Periodic Planar Disk Packings
Several conditions are given when a packing of equal disks in a torus is
locally maximally dense, where the torus is defined as the quotient of the
plane by a two-dimensional lattice. Conjectures are presented that claim that
the density of any strictly jammed packings, whose graph does not consist of
all triangles and the torus lattice is the standard triangular lattice, is at
most , where is the number of packing
disks. Several classes of collectively jammed packings are presented where the
conjecture holds.Comment: 26 pages, 13 figure
The Jamming Perspective on Wet Foams
Amorphous materials as diverse as foams, emulsions, colloidal suspensions and
granular media can {\em jam} into a rigid, disordered state where they
withstand finite shear stresses before yielding. The jamming transition has
been studied extensively, in particular in computer simulations of
frictionless, soft, purely repulsive spheres. Foams and emulsions are the
closest realizations of this model, and in foams, the (un)jamming point
corresponds to the wet limit, where the bubbles become spherical and just form
contacts. Here we sketch the relevance of the jamming perspective for the
geometry and flow of foams --- and also discuss the impact that foams studies
may have on theoretical studies on jamming.
We first briefly review insights into the crucial role of disorder in these
systems, culminating in the breakdown of the affine assumption that underlies
the rich mechanics near jamming. Second, we discuss how crucial theoretical
predictions, such as the square root scaling of contact number with packing
fraction, and the nontrivial role of disorder and fluctuations for flow have
been observed in experiments on 2D foams. Third, we discuss a scaling model for
the rheology of disordered media that appears to capture the key features of
the flow of foams, emulsions and soft colloidal suspensions. Finally, we
discuss how best to confront predictions of this model with experimental data.Comment: 7 Figs., 21 pages, Review articl