Related papers: The Rigidity of Spherical Frameworks: Swapping Blo…
For plane frameworks with reflection or rotational symmetries, where the group action is not necessarily free on the vertex set, we introduce a phase-symmetric orbit rigidity matrix for each irreducible representation of the group. We then…
In this paper we consider the effect of symmetry on the rigidity of bar-joint frameworks, spherical frameworks and point-hyperplane frameworks in $\mathbb{R}^d$. In particular we show that, under forced or incidental symmetry, infinitesimal…
We show that near densest-packing the perturbations of the HCP structure yield higher entropy than perturbations of any other densest packing. The difference between the various structures shows up in the correlations between motions of…
We study the phase behavior of hard spheres confined between two parallel hard plates using extensive computer simulations. We determine the full equilibrium phase diagram for arbitrary densities and plate separations from one to five…
Apart from not having crystallized, supercooled liquids can be considered as being properly equilibrated and thus can be described by a few thermodynamic control variables. In contrast, glasses and other amorphous solids can be arbitrarily…
In this paper we propose two guiding principles that suggest a number of conjectures (some now proved) about various forms of rigidity for moduli spaces arising in algebraic geometry. Such conjectures have group-theoretic, topological and…
We analytically and numerically characterize the structure of hard-sphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated with…
Rigidity is an emergent property of materials - it is not a feature of individual components that comprise the structure, but instead arises from interactions between many constituent parts. Recently, it has been recognized that…
We derive the equations of motion for a planar rigid body of circular shape moving in a 2D perfect fluid with point vortices using symplectic reduction by stages. After formulating the theory as a mechanical system on a configuration space…
The results of a numerical investigation of fluidized beds of spherical particles in a narrow vertical cylindrical pipe, with particular attention to the spontaneous settling along the wall, are reported. Starting from a steady fluidized…
When a hole is introduced into an elastic material, it will usually act to reduce the overall mechanical stiffness. A general ambition is to investigate whether a stiff shell around the hole can act to maintain the overall mechanical…
This paper considers the cohomology and bounded interpolation of nonstandard finite element complexes, e.g. Stokes, Hessian, Elasticity, divdiv. Compared to the standard finite element exterior calculus, the main challenge is the existence…
We show that a generic framework $(G,p)$ on the cylinder is globally rigid if and only if $G$ is a complete graph on at most four vertices or $G$ is both redundantly rigid and $2$-connected. To prove the theorem we also derive a new…
A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint…
We study static packings of frictionless and frictional spheres in three dimensions, obtained via molecular dynamics simulations, in which we vary particle hardness, friction coefficient, and coefficient of restitution. Although…
As we enter the age of designer matter - where objects can morph and change shape on command - what tools do we need to create shape-shifting structures? At the heart of an elastic deformation is the combination of dilation and distortion,…
It is well known that if there exists a finite set of convex bodies on the plane with non-overlapping interiors, then there is at least one "extremal" one among them, i.e., some one which can be continuously "taken away to the infinity"…
The stickiness effect suffered by chaotic orbits diffusing in the phase space of a dynamical system is studied in this paper. Previous works have shown that the hyperbolic structures in the phase space play an essential role in causing the…
We explain in some detail the geometric structure of spheres in any dimension. Our approach may be helpful for other homogeneous spaces (with other signatures) such as the de Sitter and anti-de Sitter spaces. We apply the procedure to the…
Unique features of particle orbits produce novel signatures of gravitational observable phenomena, and are quite useful in testing compact astrophysical objects in general relativity or modified theories of gravity. Here we observe a…