Related papers: What is the Shape of a Cupola?
The main goal of this paper is to study the extent of freedom one has in constructing quasi-copulas vs. copulas. Specifically, it exhibits three construction methods for quasi-copulas based on recent developments: a representation of…
The simple realistic model of the tippe top is considered. An averaged system of equations of motion is obtained in special evolutionary variables. Through the qualitative analysis of this system the general features of the motion of the…
An unzipping of a polyhedron P is a cut-path through its vertices that unfolds P to a non-overlapping shape in the plane. It is an open problem to decide if every convex P has an unzipping. Here we show that there are nearly flat convex…
Let $ S $ be a hyperbolic surface. We investigate the topology 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 given interval $…
There are three complete plane geometries of constant curvature: spherical, Euclidean and hyperbolic geometry. We explain how a closed oriented surface can carry a geometry which locally looks like one of these. Focussing on the hyperbolic…
This paper is a survey on the structure of manifolds with a lower Ricci curvature bound.
A surface $\Sigma$ in a 4-manifold $M$ is called flexible if any mapping class of the surface arises as the restriction of a diffeomorphism $(M,\Sigma) \to (M,\Sigma)$. We construct flexible surfaces in $\mathbb{C}P^2$ and $S^2 \times S^2$…
When a material surface is functionalized so as to acquire some type of order, functionalization of which soft condensed matter systems have recently provided many interesting examples, the modeller faces an alternative. Either the order is…
A liquid droplet is placed on a rotating helical fiber. We find that the droplet may slide down, attach or climb up the fiber. We inspect experimentally the domain of existence of these three behaviors as a function of the geometrical…
In this study, we define some new types of ruled surfaces called slant ruled surfaces. We give some characterizations for a regular ruled surface to be a slant ruled surface in Euclidean 3- space. We show that if the slant ruled surface is…
This article investigates a simple kinematical model of a disc (Disc B) rolling on the edge of a fixed disc (Disc A) to study the geometric nature of rotation. The total rotation angle $\Delta$ of Disc B after one cycle is decomposed into a…
We study the motion of self deforming bodies with non zero angular momentum when the changing shape is known as a function of time. The conserved angular momentum with respect to the center of mass, when seen from a rotating frame,…
We investigate the out-of-plane shape morphing capability of single-material elastic sheets with architected cut patterns that result in arrays of tiles connected by flexible hinges. We demonstrate that a non-periodic cut pattern can cause…
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve have attracted much interest. In the present paper, we propose a new method to construct a surface…
We consider geometric triangulations of surfaces, i.e., triangulations whose edges can be realized by disjoint locally geodesic segments. We prove that the flip graph of geometric triangulations with fixed vertices of a flat torus or a…
We investigate the topology and geometry of compact submanifolds in space forms of nonnegative curvature that satisfy a lower bound on the sectional curvature, depending only on the length of the mean curvature vector of the immersion. We…
We propose a simple mathematical model that describes the time evolution of a self-propelled object on a liquid surface using such variables as the object location, the surface concentration of active molecules and the hydrodynamic surface…
Biologically inspired pressure actuated cellular structures can alter their shape through pressure variations. Previous work introduced a computational framework for pressure actuated cellular structures which was limited to two cell rows…
This paper deals with a detail study of gravitational collapse of dust and viscous fluids under the assumptions of spherical symmetry. Our main goal is to closely analyze the horizons which arise during this gravitational phenomenon. To…
Coronal loops reveal crucial information about the nature of both coronal magnetic fields and coronal heating. The shape of the corresponding flux tube cross section and how it varies with position are especially important properties. They…