Related papers: The Rigidity of Spherical Frameworks: Swapping Blo…
Amorphous solids, or glasses, are distinguished from crystalline solids by their lack of long-range structural order. At the level of two-body structural correlations, glassformers show no qualitative change upon vitrifying from a…
This is the second paper of a series of three investigating, by numerical means, the geometric and mechanical properties of spherical bead packings under isotropic stresses. We study the effects of varying the applied pressure P (from 1 or…
A topological commutative ring is said to be rigid when for every set $X$, the topological dual of the $X$-fold topological product of the ring is isomorphic to the free module over $X$. Examples are fields with a ring topology, discrete…
The sol-gel transition is studied in two purely entropic models consisting of hard spheres in continuous three-dimensional space, with a fraction $p$ of nearest neighbor spheres tethered by inextensible bonds. When all the tethers are…
Structural organization and correlations are studied in very large packings of equally sized acrylic spheres, reconstructed in three-dimensions by means of X-ray computed tomography. A novel technique, devised to analyze correlations among…
Studies of random close packing of spheres have advanced our knowledge about the structure of systems such as liquids, glasses, emulsions, granular media, and amorphous solids. When these systems are confined their structural properties…
We present a series of experiments investigating the local microstructure of cylindrical piles composed of highly concave particles. By systematically varying particle geometry -- from spheres to strongly non-convex polypods -- as well as…
For a closed connected manifold N, we establish the existence of geometric structures on various subgroups of the contactomorphism group of the standard contact jet space J^1N, as well as on the group of contactomorphisms of the standard…
This article proposes a topological method that extracts hierarchical structures of various amorphous solids. The method is based on the persistence diagram (PD), a mathematical tool for capturing shapes of multiscale data. The input to the…
In this survey paper, we outline the proofs of the rigidity results for simple, thick, hyperbolic P-manifolds found in our three earlier papers math.GR/0506518, math.GT/0410476, and math.GR/0409586. We discuss how the arguments change in…
We study the periodic buckling patterns that emerge when elastic shells are subjected to geometric confinement. Residual swelling provides access to range of shapes (saddles, rolled sheets, cylinders, and spherical sections) which vary in…
Amorphous materials as diverse as foams, emulsions, colloidal suspensions and granular media can jam into a rigid, disordered state where they withstand finite shear stresses before yielding. Here we review the current understanding of the…
Curvature and mechanics are intimately connected for thin materials, and this coupling between geometry and physical properties is readily seen in folded structures from intestinal villi and pollen grains, to wrinkled membranes and…
When an amorphous solid is deformed cyclically, it may reach a steady state in which the paths of constituent particles trace out closed loops that repeat in each driving cycle. A remarkable variant has been noticed in simulations where the…
This paper treats the problem of the merging of formations, where the underlying model of a formation is graphical. We first analyze the rigidity and persistence of meta-formations, which are formations obtained by connecting several rigid…
A theorem of Laman gives a combinatorial characterisation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in $\bR^2$. A more general theory is developed for frameworks in $\bR^3$ whose vertices are…
It is well-known that the Kresling pattern of congruent triangles can be arranged either circularly on a cylinder of revolution or in a helical way. In both cases the resulting cylindrical structures are multi-stable. We generalize these…
In this paper we present building blocks which can explain the formation and properties both of spirals and of inner and outer rings in barred galaxies. We first briefly summarise the main results of the full theoretical description we have…
We prove a topological rigidity result for simple, thick, hyperbolic P-manifolds of dimension 2: isomorphism of the fundamental groups implies homeomorphism of the P-manifolds. An immediate application is a diagram rigidity theorem for…
Heteropolymers are ubiquitous in both synthetic systems, such as block copolymers, and biological macromolecules, including proteins and nucleic acids. Beyond their chemical composition, these polymers often exhibit spatial variations in…