Related papers: Art of Unlocking
In the paper, we give rigidity theorems when the glued space of two Alexandrov spapces with curvature bounded below is a suspension, cone or join. And we list some basic properties of joins in Appendix.
We study the manifold of clusters of nonintersecting congruent solid bodies, all touching the central ball $B\subset\mathbb{R}^{3}$ of radius one. Two main examples are clusters of balls and clusters of infinite cylinders. We introduce the…
This work focuses on the bearing rigidity theory, namely the branch of knowledge investigating the structural properties necessary for multi-element systems to preserve the inter-units bearings when exposed to deformations. The original…
The phenomenon of crumpling is common in our daily life and nature. It exhibits many interesting properties, such as ultra-tough resistance to pressure with less than 30$\%$ of volume density, power-law relation for pressure vs density, and…
In this paper we study the asymptotic behavior of a structure made of curved rods of thickness 2\delta when \delta rightarrow 0. This study is carried on within the frame of linear elasticity by using the unfolding method. It is based on…
Inspired by the recent results toward Birkhoff conjecture (a rigidity property of billiards in ellipses), we discuss two rigidity properties of conics. The first one concerns symmetries of an analog of polar duality associated with an oval,…
Granular packings display a wealth of mechanical features which are of widespread significance. One of these features is creep: the slow deformation under applied stress. Creep is common for many other amorphous materials such as many…
The sliding friction force exerted by stochastic linkers interacting with a moving filament is calculated. The elastic properties of the substrate on which the linkers are anchored are shown to strongly influence the friction force. In some…
We proof here the existence of a topological thick and thin decomposition of any closed definable thick isolated singularity germ in the spirit of the recently discovered metric thick and thin decomposition of complex normal surface…
We study how the properties of irreducibility and rigidity in digital images interact with Cartesian products, wedges, and cold and freezing sets.
In \cite{X-Z DCS1}, we introduced discrete conformal structures on surfaces with boundary via an axiomatic framework, and provided a classification of such discrete conformal structures. The present work focuses on the rigidity and…
In this paper we study the cyclicity of sliding cycles for regularized piecewise smooth visible-invisible two-folds, in the presence of singularities of the Filippov sliding vector field located away from two-folds. We obtain a slow-fast…
Structural superlubricity is an intriguing physical phenomenon, whereby sliding at a structurally incommensurate, atomically flat interface yields vanishingly small friction forces. Despite its recent experimental validation, critical…
In the present paper we survey the most recent classification results for proper biharmonic submanifolds in unit Euclidean spheres. We also obtain some new results concerning geometric properties of proper biharmonic constant mean curvature…
This is a survey on rigidity and geometrization results obtained with the help of the discrete Hilbert-Einstein functional, written for the proceedings of the "Discrete Curvature" colloquium in Luminy.
This note investigate some finiteness properties of the category U of unstable modules. One shows finiteness properties for the injective resolution of finitely generated unstable modules. One also shows a stabilization result under…
We describe recent work that extends some of the measure and topological rigidity results in dynamical systems from situations homogeneous under a Lie group to quite general manifolds.
A growing or compressed thin elastic sheet adhered to a rigid substrate can exhibit a buckling instability, forming an inward hump. Our study shows that the strip morphology depends on the delicate balance between the compression energy and…
In this paper, we give the rigidity theorem for a log morphism as an extension of a fixed scheme morphism. We also give several applications of the rigidity theorem.
In this paper, we present a cluster algorithm for the simulation of hard spheres and related systems. In this algorithm, a copy of the configuration is rotated with respect to a randomly chosen pivot point. The two systems are then…