Related papers: Sub-singularities for shaping thin sheets
This note is a continuation of the paper [2] (see references). We describe some natural pseudogroup structures on almost complex manifolds of type $m$. A kind of coherency is discussed for the sheaf of almost holomorphic functions.
Surface roughness of particle monolayer is one of its fundamental characteristics, conventionally described in terms of power spectral density. We derive a general equation for this function and demonstrate its similarity to those applied…
Porous structures are widely used in various industries because of their excellent properties. Porous surfaces have no thickness and should be thickened to sheet structures for further fabrication. However, conventional methods for…
We consider compact convex hypersurfaces contracting by functions of their curvature. Under the mean curvature flow, uniformly convex smooth initial hypersurfaces evolve to remain smooth and uniformly convex, and contract to points after…
Shape complexity is a hard-to-quantify quality, mainly due to its relative nature. Biased by Euclidean thinking, circles are commonly considered as the simplest. However, their constructions as digital images are only approximations to the…
Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…
We revisit the delamination of a solid adhesive sheet under uniaxial compression from a flat, rigid substrate. Using energetic considerations and scaling arguments we show that the phenomenology is governed by three dimensionless groups,…
This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…
Crumpling of a thin film leads to a unique stiff yet lightweight structure. The stiffness has been attributed to a complex interplay between four basic elements - smooth bends, sharp folds, localized points (developable cones), and…
We find explicit subdivision rules for all special cubulated groups. A subdivision rule for a group produces a sequence of tilings on a sphere which encode all quasi-isometric information for a group. We show how these tilings detect…
Materials featuring anomalous suppression of density fluctuations over large length scales are emerging systems known as disordered hyperuniform. The underlying hidden order renders them appealing for several applications, such as light…
Chemical, mechanical, thermal and/or electronic properties of bulk or low-dimensional materials can be engineered by introducing structural defects to form novel functionalities. When using particles irradiation, these defects can be…
This paper is motivated from a fundamental curiosity on what defines a category of object shapes. For example, we may have the common knowledge that a plane has wings, and a chair has legs. Given the large shape variations among different…
A monoid hypersurface is an irreducible hypersurface of degree d which has a singular point of multiplicity d-1. Any monoid hypersurface admits a rational parameterization, hence is of potential interest in computer aided geometric design.…
Recent experiments have imposed controlled swelling patterns on thin polymer films, which subsequently buckle into three-dimensional shapes. We develop a solution to the design problem suggested by such systems, namely, if and how one can…
Simplicial surfaces describe the incidence relations between vertices, edges and faces of triangulated 2-dimensional manifolds in a purely combinatorial way. By considering only the incidences of edges and faces, simplicial surfaces are…
We propose some new method of constructing configurations, which consists in consecutive inscribing copies of one underlying configuration. A uniform characterization of the obtained class and the one introduced in our paper untitled…
Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and…
We study the rigidity of compact submanifolds of Riemannian manifolds of arbitrary codimension that satisfy a sharp pinching condition involving the norm of the second fundamental form and the mean curvature. Without assuming that the…
We study singularities of surfaces which are given by Kenmotsu-type formula with prescribed unbounded mean curvature.