Related papers: Plumbing bijections
We show that universality in chaotic elements can be lifted to that in complex systems. We construct a globally coupled Flow lattice (GCFL), an analog of a globally coupled Map lattice (GCML). We find that Duffing GCFL shows the same…
You Only Look Once (YOLO) algorithm is a representative target detection algorithm emerging in 2016, which is known for its balance of computing speed and accuracy, and now plays an important role in various fields of human production and…
A complex of until now unknown phenomena ongoing in water was discovered in laboratory experiments, where it made impossible gravimetric measurements with the necessarily extreme precision. This behaviour of water, which we call…
Ricci flow on two dimensional surfaces is far simpler than in the higher dimensional cases. This presents an opportunity to obtain much more detailed and comprehensive results. We review the basic facts about this flow, including the…
This article introduces a newly hypothesized atmospheric phenomenon called toroh, inspired by the Brazilian regional phenomenon known as tromba de agua. The existence of the toroh, also suggested to be termed toroh, is characterized by…
Tipping points associated with bifurcations (B-tipping) or induced by noise (N-tipping) are recognized mechanisms that may potentially lead to sudden climate change. We focus here a novel class of tipping points, where a sufficiently rapid…
We show that strong coincidences of a certain many choices of control points are equivalent to overlap coincidence for the suspension tiling of Pisot substitution. The result is valid for degree $\ge 2$ as well, under certain topological…
In 2011 Enders, M\"{u}ller and Topping showed that any blow up sequence of a Type I Ricci flow near a singular point converges to a non-trivial gradient Ricci soliton, leading them to conclude that for such flows all reasonable definitions…
Knotted configurations supported by a Yang Mills fluid-field system are suggested as a model for glueballs.
Tunneling is an important physical process. The observation that particles surmount a high mountain in spite of the fact that they don't have the necessary energy cannot be explained by classical physics. However, this so called tunneling…
In this paper our first goal is to give precise definition of the L\'evy bridges with random length. Our second task is to establish the Markov property of this process with respect to its completed natural filtration and thus with respect…
The purpose of this short manuscript is to show that all point constructions that can be done via ruler and compass, can also be done with compass exclusively. If we are using compass and ruler the way we construct new points is by first…
One of the best things about geometry is that it's cool! Geometry enables us to create incredible designs and astounding patterns. This article shows how to use a simple technique (iteration) to create designs that are both cool and…
While students may find spline interpolation quite digestible, based on their familiarity with continuity of a function and its derivatives, some of its inherent value may be missed when students only see it applied to standard data…
River networks exhibit a complex ramified structure that has inspired decades of studies. Yet, an understanding of the propagation of a single stream remains elusive. Here we invoke a criterion for path selection from fracture mechanics and…
As the parameters of a piecewise-smooth system of ODEs are varied, a periodic orbit undergoes a bifurcation when it collides with a surface where the system is discontinuous. Under certain conditions this is a grazing-sliding bifurcation.…
High speed Schlieren videos were produced highlighting the fluid mechanics found in everyday objects. This video (entry 102369) was submitted as part of the Gallery of Fluid Motion 2013, which is a showcase of fluid dynamics videos.
We offer some theorems, mainly of finiteness, for certain patterns in elliptical billiards, related to periodic trajectories. For instance, if two players hit a ball at a given position and with directions forming a fixed angle in…
We study a random field obtained by counting the number of balls containing each point, when overlapping balls are thrown at random according to a Poisson random measure. We are particularly interested in the local asymptotical…
This article explores the limits of geometric construction using various tools, both classical and modern. Starting with ruler and compass constructions, we examine how adding methods such as origami, marked rulers (neusis), conic sections,…