Related papers: What is the Shape of a Cupola?
Flexible rings and rectangle structures floating at the surface of water are prone to deflect under the action of surface pressure induced by the addition of surfactant molecules on the bath. While the frames of rectangles bend inward or…
The rules in a shape grammar apply in terms of embedding to take advantage of the parts that emerge visually in the appearance of shapes. While the shapes are kept unanalyzed as a computation moves forward, part-structures for shapes can be…
We study topological properties of automorphisms of 4-dimensional torus generated by integer symplectic matrices. The main classifying element is the structure of the topology of a foliation generated by unstable leaves of the automorphism.…
Consider a deformable body immersed in an incompressible fluid that is randomly stirred. Sticking to physical situations in which the body departs only slightly from its spherical shape, we investigate the deformations of the body. The…
The coupled attitude and orbit dynamics of solar sails is studied. The shape of the sail is a simplified quasi-rhombic-pyramid that provides the structure helio-stablility properties. After adimensionalisation, the system is put in the form…
The role of porous structure and glass density in response to compressive deformation of amorphous materials is investigated via molecular dynamics simulations. The disordered, porous structures were prepared by quenching a high-temperature…
Motivated by applications in CNC machining, we provide a characterization of surfaces which are enveloped by a one-parametric family of congruent rotational cones. As limit cases, we also address developable surfaces and ruled surfaces. The…
We address the unsolved problem of unfolding prismatoids in a new context, viewing a "topless prismatoid" as a convex patch---a polyhedral subset of the surface of a convex polyhedron homeomorphic to a disk. We show that several natural…
Liquids in oil-bearing porous media assume complex shapes that depend on the reservoir characteristics and the wetting properties of the liquid. The wide variation in the geometry of rock formations makes it difficult to accurately predict…
A spherical polyhedron surface is a triangulated surface obtained by isometric gluing of spherical triangles. For instance, the boundary of a generic convex polytope in the 3-sphere is a spherical polyhedron surface. This paper investigates…
Let $S$ be a complete flat surface, such as the Euclidean plane. We determine the homeomorphism class of the space of all curves on $S$ which start and end at given points in given directions and whose curvatures are constrained to lie in a…
We establish the existence of a cusp in the curvature of a solid sheet at its contact with a liquid subphase. We study two configurations in floating sheets where the solid-vapor-liquid contact line is a straight line and a circle,…
Many objects in nature and industry are wrapped in a thin sheet to enhance their chemical, mechanical, or optical properties. There are similarly a variety of methods for wrapping, from pressing a film onto a hard substrate, to using…
We define a notion for unfolding smooth, ruled surfaces, and prove that every smooth prismatoid (the convex hull of two smooth curves lying in parallel planes), has a nonoverlapping "volcano unfolding." These unfoldings keep the base…
A smooth T-surface can be thought of as a generalization of a surface of revolution in such a way that the axis of rotation is not fixed at one point but rather traces a smooth path on the base plane. Furthermore, the action, by which the…
We analyze the limit of the p-form Laplacian under a collapse, with bounded sectional curvature and bounded diameter, to a smooth limit space. As an application, we characterize when the p-form Laplacian has small positive eigenvalues in a…
Most galaxies have a warped shape when they are seen from an edge-on point of view. The reason for this curious form is not completely known so far and in this work we apply dynamical system tools to contribute to its explanation. Starting…
We introduce an alternative way of constructing continuous flexible tubes and tubular structures based on a discrete, semi-discrete and smooth construction of surfaces known as T-hedra in the discrete case and profile-affine surfaces in the…
A new formula is obtained in algebraic topology, in terms of Betti numbers, and a new method, called the spinal method, is suggested and developed for generating quadrangulations of closed orientable surfaces. Those surfaces arise as the…
It is well known that celestial bodies tend to be spherical due to gravity and that rotation produces deviations from this sphericity. We discuss what is known and expected about the shape of black holes' horizons from their formation to…