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Extracting shape information from object bound- aries is a well studied problem in vision, and has found tremen- dous use in applications like object recognition. Conversely, studying the space of shapes represented by curves satisfying…
Polymeric particles are strong candidates for designing artificial materials capable of emulating the complex twisting-based functionality observed in biological systems. In this letter, we provide the first detailed investigation of the…
We consider the problem of a sphere rolling of a curved surface and solve it by mapping it to the precession of a spin 1/2 in a magnetic field of variable magnitude and direction. The mapping can be of pedagogical use in discussing both…
A coupling onset of the cyclone upward and rotation flows is experimentally demonstrated in a little bottle. The rotating flow provides a pressure increase in the outer part of the rotating flow by its centrifugal force. When a gradient of…
The mechanical properties of thermally excited two-dimensional crystalline membranes can depend dramatically on their geometry and topology. A particularly relevant example is the effect on the crumpling transition of holes in the membrane.…
A loop of chain can move along its own tangents, maintaining a steady shape. An open-ended chain undergoing a nontrivial motion must change its shape. One consequence is that chains pulled around objects will fail to follow the contours of…
To consider the entanglement between the spatial region $A$ and its complement in a QFT, we need to assign a Hilbert space $\mathcal{H}_A$ to the region, by making a certain choice on the boundary $\partial A$. We argue that a small…
Manifolds occur naturally as configuration spaces of robotic systems. They provide global descriptions of local coordinate systems that are common tools in expressing positions of robots. The purpose of this survey is threefold. Firstly, we…
A non-unitary version of quantum scattering is studied via an exactly solvable toy model. The model is merely asymptotically local since the smooth path of the coordinate is admitted complex in the non-asymptotic domain. At any real…
Tangent points, especial dynamics existing only in piecewise-smooth systems, usually have dynamical properties like equilibria of smooth systems. Loops connecting tangent points own partly properties of limit cycles and homoclinic loops of…
We show that in codimension at least 3, spaces of locally flat topological embeddings of manifolds are correctly modelled by derived spaces of maps between their configuration categories (under mild smoothability conditions). That general…
Given a saddle fixed point of a surface diffeomorphism, its stable and unstable curves $W^S$ and $W^U$ often form a homoclinic tangle. Given such a tangle, we use topological methods to find periodic points of the diffeomorphism, using only…
Topology, a well-established concept in mathematics, has nowadays become essential to describe condensed matter. At its core are chiral electron states on the bulk, surfaces and edges of the condensed matter systems, in which spin and…
The aim of this paper is to study dynamical and topological properties of a flow in the region of influence of an isolated non-saddle set or a $W$-set in a manifold. These are certain classes of compact invariant sets in whose vicinity the…
It has long been known to mathematicians and physicists that while a full rotation in three-dimensional Euclidean space causes tangling, two rotations can be untangled. Formally, an untangling is a based nullhomotopy of the double-twist…
We investigate the occurrence of topologically protected waves in classical fluids confined on curved surfaces. Using a combination of topological band theory and real space analysis, we demonstrate the existence of a system-independent…
We introduce an elementary transformation called flips on tilings by squares and triangles and conjecture that it connects any two tilings of the same region of the Euclidean plane.
Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. The various proposals in the literature are usually motivated by…
The flow of viscous fluids is considered as the aggregation of the motion of fluid particles when the fluid is conceived to be made up by an infinite number of particles. As an alternative of this conventional model, fluid motion could be…
Quantum entanglement occurs not just in discrete systems such as spins, but also in the spatial wave functions of systems with more than one degree of freedom. It is easy to introduce students to entangled wave functions at an early stage,…