Related papers: On Exponents of Thickness in Geometry Rigidity Ine…
The aim of this paper is to present some properties of reduced spherical convex bodies on the two-dimensional sphere $S^2$. The intersection of two different non-opposite hemispheres is called a lune. By its thickness we mean the distance…
In this paper, we first give some new characterizations of geodesic spheres in the hyperbolic space by the condition that hypersurface has constant weighted shifted mean curvatures, or constant weighted shifted mean curvature ratio, which…
The aim of the paper is to investigate the rigidity and the deformability of pseudoholomorphic curves in the nearly K{\"a}hler sphere $\mathbb{S}^6,$ among minimal surfaces in spheres. Under various assumptions we describe the moduli space…
We prove rigidity results involving the Hawking mass for surfaces immersed in a $3$-dimensional, complete Riemannian manifold $(M,g)$ with non-negative scalar curvature (resp. with scalar curvature bounded below by $-6$). Roughly, the main…
Wall-roughness induces extra drag in wall-bounded turbulent flows. Mapping any given roughness geometry to its fluid dynamic behaviour has been hampered by the lack of accurate and direct measurements of skin-friction drag. Here the…
Many compliant shell mechanisms are periodically corrugated or creased. Being thin, their preferred deformation modes are inextensional, i.e., isometric. Here, we report on a recent characterization of the isometric deformations of periodic…
first-principles numerical simulation model for crumpling of a stiff tethered membrane is introduced. In our model membranes, wrinkles, ridge formation, ridge collapse, as well as the initiation of stiffness divergence, are observed. The…
It is conjectured that all decomposable (i.e. interior can be triangulated without adding new vertices) polyhedra with vertices in convex position are infinitesimally rigid and only recently has it been shown that this is indeed true under…
Recently, a simple and elegant "dimple" model was introduced by McMeeking et al. (Adv Eng Mat 12(5), 389-397, 2010) to show a mechanism for a bistable adhesive system involving a surface with a shallow depression. The system shows, at least…
Pastewka & Robbins (PNAS, 111(9), 3298-3303, 2014) recently have proposed a criterion to distinguish when two surfaces will stick together or not, and suggested it shows a large conflict with asperity theories. It is found that their…
A general framework is developed to study the deformation and stress response in F{\"o}ppl-von K{\'a}rm{\'a}n shallow shells for a given distribution of defects, such as dislocations, disclinations, and interstitials, and metric anomalies,…
In this paper we present a rigidity theorem for locally isometric hypersurfaces with a curvature restriction in de Sitter space. This is an analogue to the case for Riemannian space forms given by Guan and Shen in [5].
We discuss infinitesimal isometries of the middle surfaces and present some characteristic conditions for a function to be the normal component of an infinitesimal isometry. Our results show that those characteristic conditions depend on…
We perform direct numerical simulations of turbulent flow at friction Reynolds number $Re_\tau \approx 500-2000$ grazing over perforates plates with moderate viscous-scaled orifice diameter $d^+\approx40$--$160$ and analyse the relation…
Solid interfaces have intrinsic elasticity. However, in most experiments, this is obscured by bulk stresses. Through microscopic observations of the contact-line geometry of a partially wetting droplet on an anisotropically stretched…
For the Bach-flat closed manifold with positive scalar curvature, we prove a rigidity result under a given inequality involving the Weyl curvature and the traceless Ricci curvature. Moveover, under an inequality involving…
The objective of this paper is to help shedding some light on the nature and the properties of the cold structures formed via thermal instability in the magnetized atomic interstellar medium. To this end, we searched for clumps formed in…
Soft solids exhibit instability and develop surface undulations due to surface effects, a phenomenon known as the elastic Plateau-Rayleigh (PR) instability, driven by the interplay of surface and bulk elasticity. Previous studies on the PR…
At the molecular scale there are strong attractive interactions between surfaces, yet few macroscopic surfaces are sticky. Extensive simulations of contact by adhesive surfaces with roughness on nanometer to micrometer scales are used to…
Nonequilibrium molecular dynamics simulations are used to study the shear thinning behavior of immiscible symmetric polymer blends. The phase separated polymers are subjected to a simple shear flow imposed by moving a wall parallel to the…