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

A \emph{stacked triangulation} of a $d$-simplex $\mathbf{o}=\{1,\ldots,d+1\}$ ($d\geq 2$) is a triangulation obtained by repeatedly subdividing a $d$-simplex into $d+1$ new ones via a new vertex (the case $d=2$ is known as an Appolonian…

We prove that if $G$ is the graph of a connected triangulated $(d-1)$-manifold, for $d\geq 3$, then $G$ is generically globally rigid in $\mathbb R^d$ if and only if it is $(d+1)$-connected and, if $d=3$, $G$ is not planar. The special case…

We extend classical finite-dimensional Fenichel theory in two directions to infinite dimensions. Under comparably weak assumptions we show that the solution of an infinite-dimensional fast-slow system is approximated well by the…

Let $M$ be the space of triangles, defined up to shifts, rotations and dilations. We define two maps $f:M\to M$ and $g:M\to M$. The map $f$ corresponds to a triangle of perimeter $\pi$ the triangle with angles numerically equal to edges of…

The determination of a dynamic law of cut is complex and often very difficult to develop. Several formulations were developed, in very complex ways being given that 3 AD crosses from there, the number of variables is much higher than out of…

We prove that if G is a graph without 3-cycles and 4-cycles, then the discrete cubical homology of G is trivial in dimension d, for all d\ge 2. We also construct a sequence { G_d } of graphs such that this homology is non-trivial in…

Self-consistent (non-)abelian statistics in 2+1D are classified by modular tensor categories (MTC). In recent works, a simplified axiomatic approach to MTCs, based on fusion coefficients $N^{ij}_k$ and spins $s_i$, was proposed. A numerical…

Let $tsp(G)$ denote the length of a shortest travelling salesman tour in a graph $G$. We prove that for any $\varepsilon>0$, there exists a simple $2$-connected planar cubic graph $G_1$ such that $tsp(G_1)\ge…

In this note, we develop fast and deterministic dimensionality reduction techniques for a family of subspace approximation problems. Let $P\subset \mathbbm{R}^N$ be a given set of $M$ points. The techniques developed herein find an $O(n…

Dynamical System (DS)-based closed-loop control is a simple and effective way to generate reactive motion policies that well generalize to the robotic workspace, while retaining stability guarantees. Lately the formalism has been expanded…

We analyze fast diagonal methods for simple bilevel programs. Guided by the analysis of the corresponding continuous-time dynamics, we provide a unified convergence analysis under general geometric conditions, including H\"olderian growth…

Nominal two-dimensional (2D) shear layers have been studied extensively, and their principal dynamics are well understood. In practical configurations, however, the behavior of such shear layers is affected by proximal surfaces. In this…

A new numerical framework, based on the use of a simple first order strongly hyperbolic evolution equations, is introduced and tested in case of 4-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that…

We present numerical simulation of 2D turbulent flow using a new model for the subgrid scales which are computed using a dynamic equation linking the subgrid scales with the resolved velocity. This equation is not postulated, but derived…

A model of simplicial quantum gravity in three dimensions(3D) was investigated numerically based on the technique of dynamical triangulation (DT). We are concerned with the genus of surfaces appearing on boundaries (i.e., sections) of a 3D…

We consider the two-dimensional (2D) flow in a flat free-slip surface that bounds a three-dimensional (3D) volume in which the flow is turbulent. The equations of motion for the two-dimensional flow in the surface are neither compressible…

This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…

We theoretically explore the dynamical properties of a first-order dissipative phase transition in coherently driven Bose-Hubbard systems, describing, e.g., lattices of coupled nonlinear optical cavities. Via stochastic trajectory…

Numerical simulations of kinematic dynamo action in steady and 3-d ABC flows are presented with special focus on growth rates and multiple periods of the prescribed velocity field. It is found that the difference in growth rate is due to…

In two-dimensional space, we investigate the slow dynamics of multiple localized spots with oscillatory tails in a specific three-component reaction-diffusion system, whose key feature is that the spots attract or repel each other…