In this review article we discuss a number of recent results concerning wild weak solutions of
the incompressible Euler and Navier–Stokes equations. These results build on the …

Dynamical models underpin our ability to understand and predict the behaviour of natural
systems. Whether dynamical models are developed from first-principles derivations or from …

Starting from simple notions of paper folding, a review of current challenges regarding folds
and structures is presented. A special focus is dedicated to folded tessellations which are …

Developable surfaces are those that can be made by smoothly bending flat pieces without
stretching or shearing. We introduce a definition of developability for triangle meshes which …

In this Letter we explore and develop a simple set of rules that apply to cutting, pasting, and
folding honeycomb lattices. We consider origami-like structures that are extrinsically flat …

We use a regular arrangement of kirigami elements to demonstrate an inverse design
paradigm for folding a flat surface into complex target configurations. We first present a …

The question whether one can recover the shape of a geometric object from its Laplacian
spectrum ('hear the shape of the drum') is a classical problem in spectral geometry with a …

This paper develops a shape space framework for collision-aware geometric modeling,
where basic geometric operations automatically avoid inter-penetration. Shape spaces are a …

We study the low-regularity (in-) extendibility of spacetimes within the synthetic-geometric
framework of Lorentzian length spaces developed in Kunzinger and Sämann (Ann Glob …

Materials that can expand and collapse, fold, and transform into a variety of shapes have
attracted significant interest and have applications in the design of flexible electronics, color …