相关论文: Beta-Skeletons have Unbounded Dilation
We study, both with numerical simulations and theoretical methods, a cellular automata model for continuum equations describing growth processes in the presence of an external flux of particles. As a result of local instabilities we find a…
Through controlled numerical simulations in a one dimensional fiber bundle model with local stress concentration, we established an inverse correlation between the strength of the material and the cracks which grow inside it - both the…
If $G$ is a more than one tough graph on $n$ vertices with $\delta\ge \frac{n}{2}-a$ for a given $a>0$ and $n$ is large enough then $G$ is hamiltonian.
This paper considers the issue of modeling fractional data observed in the interval [0,1), (0,1] or [0,1]. Mixed continuous-discrete distributions are proposed. The beta distribution is used to describe the continuous component of the model…
A Gilbert tessellation arises by letting linear segments (cracks) in the plane unfold in time with constant speed, starting from a homogeneous Poisson point process of germs in randomly chosen directions. Whenever a growing edge hits an…
Let $G$ be a non-abelian finite simple group. In addition, let $\Delta_G$ be the intersection graph of $G$, whose vertices are the proper nontrivial subgroups of $G$, with distinct subgroups joined by an edge if and only if they intersect…
Formation and evolution of fragmentation instabilities in fractal islands, obtained by deposition of silver clusters on graphite, are studied. The fragmentation dynamics and subsequent relaxation to the equilibrium shapes are controlled by…
A droplet of surfactant spreading on an ultrasoft ($E \lesssim 100$ Pa) gel substrate will produce capillary fractures at the gel surface; these fractures originate at the contact-line and propagate outwards in a starburst pattern. There is…
We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…
We formulate a construction of type-I fracton models based on gauging planar subsystem symmetries of topologically ordered two dimensional layers that have been stacked in three ambient spatial dimensions. Via our construction, any defect…
An eigenfunction of the Laplacian on a metric (quantum) graph has an excess number of zeros due to the graph's non-trivial topology. This number, called the nodal surplus, is an integer between 0 and the graph's first Betti number $\beta$.…
We present an unified approach on the behavior of two random growth models (external DLA and internal DLA) on infinite graphs, the second one being an internal counterpart of the first one. Even though the two models look pretty similar,…
We analyse linear stability of interfacial waves in an idealised model of an aluminium reduction cell consisting of two stably stratified liquid layers which carry a vertical electric current in a collinear external magnetic field. If the…
We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail.…
We show that a length scale xi can be extracted from the spatial correlations of the "steep cliffs" that appear on fracture surface. Above xi, the slope amplitudes are uncorrelated and the fracture surface is mono-affine. Below xi,…
Every graph of size $q$ (the number of edges) and minimum degree $\delta$ is hamiltonian if $q\le\delta^2+\delta-1$. The result is sharp.
Fracton theories possess exponentially degenerate ground states, excitations with restricted mobility, and nontopological higher-form symmetries. This paper shows that such theories can be defined on arbitrary spatial lattices in three…
In this paper we study the Alexander dual of a vertex decomposable simplicial complex. We define the concept of a vertex splittable ideal and show that a simplicial complex $\Delta$ is vertex decomposable if and only if $I_{\Delta^{\vee}}$…
The stability number of a graph G is the cardinality of a stability system of G (that is of a stable set of maximum size of G). A graph is alpha-stable if its stability number remains the same upon both the deletion and the addition of any…
There is a general agreement that galaxy structures exhibit fractal properties, at least up to some small scale. However the presence of an eventual crossover towards homogenization, as well as the exact value of the fractal dimension, are…