Related papers: Art of Unlocking
We study geometric rigidity of a class of fractals, which is slightly larger than the collection of self-conformal sets. Namely, using a new method, we shall prove that a set of this class is contained in a smooth submanifold or is totally…
A rigidity theory is developed for bar-joint frameworks in $\mathbb{R}^{d+1}$ whose vertices are constrained to lie on concentric $d$-spheres with independently variable radii. In particular, combinatorial characterisations are established…
We study the motion of elastic networks driven over a random substrate. Our model which includes local friction forces leads to complex dynamical behavior. We find a transition to a sliding state which belongs to a new universality class.…
Depletion-induced aggregation of rods enhanced by clustering is observed to produce a novel model of attractive pairs of rods separated by a line of spheres in a quasi-2D, vertically-shaken, granular gas of rods and spheres. We show that…
We review on the recent developments for the computation of scattering amplitudes, with attention to the on-shell formalisms and unitarity-based methods.
When implementing a non-continuous controller for a cyber-physical system, it may happen that the evolution of the closed-loop system is not anymore piecewise differentiable along the trajectory, mainly due to conditional statements inside…
Packing problems, which ask how to arrange a collection of objects in space to meet certain criteria, are important in a great many physical and biological systems, where geometrical arrangements at small scales control behaviour at larger…
We prove a topological rigidity theorem for closed hypersurfaces of the Euclidean sphere and of an elliptic space form. It asserts that, under a lower bound hypothesis on the absolute value of the principal curvatures, the hypersurface is…
In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective transformation of the plane.
We consider a class of overdetermined problems in rotationally symmetric spaces, which reduce to the classical Serrin's overdetermined problem in the case of the Euclidean space. We prove some general integral identities for rotationally…
We present the results of an experimental investigation into buoyant rigid spheres rising through highly concentrated collections of hydrated hydrogel particles. The volume fraction of particles is such that the mechanical properties of the…
We present a computational study of sliding between gold clusters and a highly oriented pyrolytic graphite substrate, a material system that exhibits ultra-low friction due to structural lubricity. By means of molecular dynamics, it is…
Elasticity has long been regarded as a property exclusive to material media. Here we uncover its hidden existence in the spin degree of freedom. We introduce spin elasticity-an intrinsic mechanism that governs recoverable deformation of…
It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or 'fusion') of two structures which are stable when separately analyzed. The compound elastic structure has two degrees of…
In this paper we first survey some basic results in the cohomology of finite groups, and then discuss recent work on constructing free actions of finite groups on products of spheres.
This is an invited commentary on "Geometrically incompatible confinement of solids", B. Davidovitch, Y. Sun and G. M. Grason (PNAS, doi:10.1073/pnas.1815507116 , arxiv:1809.06919).
In this paper, we characterize round spheres in the Euclidean space under some suitable conditions on the r-mean curvature.
We investigate the formation of cluster crystals with multiply occupied lattice sites on a spherical surface in systems of ultra-soft particles interacting via repulsive, bounded pair potentials. Not all interactions of this kind lead to…
We propose a sliding surface for systems on the Lie group $SO(3)\times \mathbb{R}^3$ . The sliding surface is shown to be a Lie subgroup. The reduced-order dynamics along the sliding subgroup have an almost globally asymptotically stable…
In this paper we review some recent results concerning inverse problems for thin elastic plates. The plate is assumed to be made by non-homogeneous linearly elastic material belonging to a general class of anisotropy. A first group of…