Related papers: Conical defects in growing sheets
Macroscopic two-dimensional sonic crystals with inversion symmetry are studied to reveal higher-order topological physics in classical wave systems. By tuning a single geometry parameter, the band topology of the bulk and the edges can be…
We study mapping cones and their dual cones of positive maps of the n by n matrices into itself. For a natural class of cones there is a close relationship between maps in the cone, super-positive maps, and separable states. In particular…
Composed of square particles, the tetratic phase is characterised by a four-fold symmetry with quasi-long-range orientational order but no translational order. We construct the elastic free energy for tetratics and find a closed form…
Growth-induced instabilities are ubiquitous in biological systems and lead to diverse morphologies in the form of wrinkling, folding, and creasing. The current work focusses on the mechanics behind growth-induced wrinkling instabilities in…
We generalize the spherical collapse model for the formation of bound objects to apply in a Universe with arbitrary positive cosmological constant. We calculate the critical condition for collapse of an overdense region and give exact…
We give sufficient conditions for a noncompact Riemannian manifold, which has quadratic curvature decay, to have finite topological type with ends that are cones over spherical space forms.
Let $M$ be an open (i.e. complete and noncompact) manifold with nonnegative Ricci curvature. In this paper, we study whether the volume growth order of $M$ is always greater than or equal to the dimension of some (or every) asymptotic cone…
Given a smooth convex cone in the Euclidean $(n+1)$-space ($n\geq2$), we consider strictly mean convex hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicularly. If…
Ordered phases on curved substrates experience a complex interplay of ordering and intrinsic curvature, commonly producing frustration and singularities. This is an especially important issue in crystals as ever-smaller scale materials are…
Predicting the large-amplitude deformations of thin elastic sheets is difficult due to the complications of self-contact, geometric nonlinearities, and a multitude of low-lying energy states. We study a simple two-dimensional setting where…
A beer bottle or soda can on a table, when slightly tipped and released, falls to an upright position and then rocks up to a somewhat opposite tilt. Superficially this rocking motion involves a collision when the flat circular base of the…
The shape of a liquid drop placed in a cone is analyzed macroscopically. Depending on the values of the cone opening angle, the Young angle and the line tension four different interfacial configurations may be realized. The phase diagram in…
Leaves and flowers frequently have a characteristic rippling pattern at their edges. Recent experiments found similar patterns in torn plastic. These patterns can be reproduced by imposing metrics upon thin sheets. The goal of this paper is…
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
If we fix the angles at the vertices of a convex planar $n$-gon, the lengths of its edges must satisfy two linear constraints in order for it to close up. If we also require unit perimeter, our vectors of $n$ edge lengths form a convex…
Sulci are localized furrows on the surface of soft materials that form by a compression-induced instability. We unfold this instability by breaking its natural scale and translation invariance, and compute a limiting bifurcation diagram for…
We use boundary-integral methods to compute the time-dependent deformation of a drop of dielectric fluid immersed in another dielectric fluid in a uniform electric field E. Steady state theory predicts, when the permittivity ratio, \beta,…
We consider a free boundary problem for a system of PDEs, modeling the growth of a biological tissue. A morphogen, controlling volume growth, is produced by specific cells and then diffused and absorbed throughout the domain. The geometric…
Gravitational collapse of the cylindrical elongated cloud is studied by numerical magnetohydrodynamical simulations. In the infinitely long cloud in hydrostatic configuration, small perturbations grow by the gravitational instability. The…
We investigate the growth of a crystal that is built by depositing cubes onto the inside of a corner. The interface of this crystal evolves into a limiting shape in the long-time limit. Building on known results for the corresponding…