相关论文: Dynamical Systems of Simplices in Dimension 2 or 3

Let $S$ be a $k$-colored (finite) set of $n$ points in $\mathbb{R}^d$, $d\geq 3$, in general position, that is, no {$(d + 1)$} points of $S$ lie in a common $(d - 1)$}-dimensional hyperplane. We count the number of empty monochromatic…

We study the dynamical symmetries of a class of two-dimensional superintegrable systems on a 2-sphere, obtained by a procedure based on the Marsden-Weinstein reduction, by considering its shape-invariant intertwining operators. These are…

This paper is an attempt to classify finite-time singularities of PDEs. Most of the problems considered describe free-surface flows, which are easily observed experimentally. We consider problems where the singularity occurs at a point, and…

Let $S \subset \mathbb{R}^2$ be a set of $n$ sites, where each $s \in S$ has an associated radius $r_s > 0$. The disk graph $D(S)$ is the undirected graph with vertex set $S$ and an undirected edge between two sites $s, t \in S$ if and only…

We are interested in a complete characterization of the contact-line singularity of thin-film flows for zero and nonzero contact angles. By treating the model problem of source-type self-similar solutions, we demonstrate that this…

Let $G$ be a directed graph with $n$ vertices and $m$ edges, embedded on a surface $S$, possibly with boundary, with first Betti number $\beta$. We consider the complexity of finding closed directed walks in $G$ that are either contractible…

Spatially extended systems, such as channel or pipe flows, are often equivariant under continuous symmetry transformations, with each state of the flow having an infinite number of equivalent solutions obtained from it by a translation or a…

We study the time complexity of the discrete $k$-center problem and related (exact) geometric set cover problems when $k$ or the size of the cover is small. We obtain a plethora of new results: - We give the first subquadratic algorithm for…

Following the analysis of tachyons and orbifold flips described in hep-th/0412337, we study nonsupersymmetric analogs of the supersymmetric conifold singularity and show using their toric geometry description that they are nonsupersymmetric…

A model describing Ising spins with short range interactions moving randomly in a plane is considered. In the presence of a hard core repulsion, which prevents the Ising spins from overlapping, the model is analogous to a dynamically…

We describe numerical simulations and analyses of a quasi-one-dimensional (Q1D) model of glassy dynamics. In this model, hard rods undergo Brownian dynamics through a series of narrow channels connected by $J$ intersections. We do not allow…

In this paper we study coupled fast-slow ordinary differential equations (ODEs) with small time scale separation parameter $\epsilon$ such that, for every fixed value of the slow variable, the fast dynamics are sufficiently chaotic with…

Let $v$ be a solution of the axially symmetric Navier-Stokes equation. We determine the structure of certain (possible) maximal singularity of $v$ in the following sense. Let $(x_0, t_0)$ be a point where the flow speed $Q_0 = |v(x_0,…

A fine mixed subdivision of a (d-1)-simplex T of size n gives rise to a system of ${d \choose 2}$ permutations of [n] on the edges of T, and to a collection of n unit (d-1)-simplices inside T. Which systems of permutations and which…

For a continuous semicascade on a metrizable compact set $\Omega $, we consider the weak$^{*}$ convergence of generalized operator ergodic means in ${\rm End}\, \, C^{*} (\Omega)$. We discuss conditions on the dynamical system under which…

The paper studies the relationship between diffraction and dynamics for uniformly discrete ergodic point processes in real spaces. This relationship takes the form of an isometric embedding of two L^2 spaces. Diffraction (or equivalently…

Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…

Swimming in circles occurs in a variety of situations at low Reynolds number. Here we propose a simple model for a swimmer that undergoes circular motion, generalising the model of a linear swimmer proposed by Najafi and Golestanian (Phys.…

By a sequence of numerical experiments we demonstrate that generic triangulations of the $D-$sphere for $D>3$ contain one {\it singular} $(D-3)-$simplex. The mean number of elementary $D-$simplices sharing this simplex increases with the…

This work is a continuation of [13]. We study the linear disjointness between higher-order oscillating sequences and nonlinear dynamical systems. Specifically, we prove that any oscillating sequence of order $m=d+k-1$ and any simple…