相关论文: Folded Goursat surface and banana-shaped seedpod

Since the set of volumes of hyperbolic 3-manifolds is well ordered, for each fixed g there is a genus-g surface bundle over the circle of minimal volume. Here, we introduce an explicit family of genus-g bundles which we conjecture are the…

Cosserat rod theory is the popular approach to modeling ferromagnetic soft robots as 1-Dimensional (1D) slender structures in most applications, such as biomedical. However, recent soft robots designed for locomotion and manipulation often…

The process of self-morphing in curved surfaces found in nature, such as with the growth of flowers and leaves, has generated interest in the study of self-morphing bilayers, which has been used in many soft robots or switchers. However,…

Confined thin structures are ubiquitous in nature. Spatial and length constraints have led to a number of novel packing strategies at both the micro-scale, as when DNA packages inside a capsid, and the macro-scale, seen in plant root…

This paper introduces a new type of open book decomposition for a contact three-manifold with a specified characteristic foliation $\mathcal{F}_\xi$ on its boundary. These \textit{foliated open books} offer a finer tool for studying contact…

Polymer-grafted nanoparticles are versatile building blocks that self-assemble into a rich diversity of mesostructures. Coarse-grained molecular simulations have commonly accompanied experiments by resolving structure formation pathways and…

Let $g_t$ be a smooth 1-parameter family of negatively curved metrics on a closed hyperbolic 3-manifold $M$ starting at the hyperbolic metric. We construct foliations of the Grassmann bundle $Gr_2(M)$ of tangent 2-planes whose leaves are…

The design of complex materials and the formation of specific patterns often arise from the properties of the individual building blocks. In this respect, colloidal systems offer a unique opportunity because nowadays they can be synthesized…

Shape-morphing robots have shown benefits in industrial grasping. We propose form-flexible grippers for adaptive grasping. The design is based on the hybrid jamming and suction mechanism, which deforms to handle objects that vary…

Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular…

The category of exploded torus fibrations is an extension of the category of smooth manifolds in which some adiabatic limits look smooth. (For example, the limits considered in tropical geometry appear smooth, also degenerations…

The bistability of embedded elements provides a natural route through which to introduce reprogrammability to elastic meta-materials. One example of this is the soft morphable sheet, in which bistable elements that can be snapped up or…

The coupling of geometrical and electronic properties is a promising venue to engineer conduction properties in graphene. Confinement added to strain allows for interplay of different transport mechanisms with potential device applications.…

The folding of paper, hide, and woven fabric has been used for millennia to achieve enhanced articulation, curvature, and visual appeal for intrinsically flat, two-dimensional materials. For graphene, an ideal two-dimensional material,…

The ability to manufacture tailored graphene nanostructures is a key factor to fully exploit its enormous technological potential. We have investigated nanostructures created in graphene by swift heavy ion induced folding. For our…

Over the past few decades, efforts have been made towards robust robotic grasping, and therefore dexterous manipulation. The soft gripper has shown their potential in robust grasping due to their inherent properties-low, control complexity,…

We review the relations between compact complex manifolds carrying various types of Hermitian metrics (K\"ahler, balanced or {\it strongly Gauduchon}) and those satisfying the $\partial\bar\partial$-lemma or the degeneration at $E_1$ of the…

Grasping is an essential capability for most robots in practical applications. Soft robotic grippers are considered as a critical part of robotic grasping and have attracted considerable attention in terms of the advantages of the high…

A key challenge in robotics is to create efficient methods for grasping objects with diverse shapes, sizes, poses, and properties. Grasping with hand-like end effectors often requires careful selection of hand orientation and finger…

Piecewise Euclidean structures (identified solid Euclidean polyhedra) on topological 3-dimensional manifolds and pseudo-manifolds are constructed so that they admit pseudo-foliations, a generalized type of foliation. The construction of…