Related papers: The sandpile identity element on an ellipse
Diversities are a generalization of metric spaces, where instead of the non-negative function being defined on pairs of points, it is defined on arbitrary finite sets of points. Diversities have a well-developed theory. This includes the…
Properties of several sorts of lattices of convex subsets of R^n are examined. The lattice of convex sets containing the origin turns out, for n>1, to satisfy a set of identities strictly between those of the lattice of all convex subsets…
On the circle of radius $R$ centred at the origin, consider a ``thin'' sector about the fixed line $y = \alpha x$ with edges given by the lines $y = (\alpha \pm \epsilon) x$, where $\epsilon = \epsilon_R \rightarrow 0$ as $ R \to \infty $.…
In this work we address the statistical periodicity phenomenon on a coupled map lattice. The study was done based on the asymptotic binary patterns. The pattern multiplicity gives us the lattice information capacity, while the entropy rate…
We study the Abelian sandpile model (ASM), a process where grains of sand are placed on a graph's vertices. When the number of grains on a vertex is at least its degree, one grain is distributed to each neighboring vertex. This model has…
In this paper we address the characterization of the structure of condensed materials, periodic and non-periodic. Carrying out an extensive study of over 7000 different groundstate structures of a 2D lattice model of binary packing, we find…
We introduce a graph structure on Euclidean polytopes. The vertices of this graph are the $d$-dimensional polytopes contained in $\mathbb{R}^d$ and its edges connect any two polytopes that can be obtained from one another by either…
Seidel switching is a classical operation on graphs which plays a central role in the theory of two-graphs, signed graphs, and switching classes. In this paper we focus on those switches which leave a given graph invariant up to…
It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…
Consider the network of elements connected by adjacency in atomic number and periodic table column. If all elements except H-He are connected by identical springs and constrained to a z-spiral in 2D, a map sans spring-crossing results for…
Consider a random three-coordinate lattice of spherical topology having 2v vertices and being densely covered by a single closed, self-avoiding walk, i.e. being equipped with a Hamiltonian cycle. We determine the number of such objects as a…
The origin of the large-scale stripe pattern of epitaxial silicene on the ZrB$_2$(0001) surface observed by scanning tunneling microscope experiments is revealed by first-principles calculations. Without stripes, the…
We study the spectral stability of a 2D discrete Schr\"{o}dinger equation on a square lattice, in the simultaneous presence of a fractional Laplacian and $\cal{PT}$ symmetry. For that purpose, we compute the plane-wave spectrum in closed…
By a twenty year old result of Ralph Freese, an $n$-element lattice $L$ has at most $2^{n-1}$ congruences. We prove that if $L$ has less than $2^{n-1}$ congruences, then it has at most $2^{n-2}$ congruences. Also, we describe the…
Silicene, a monolayer of silicon atoms tightly packed into a two-dimensional honeycomb lattice, is the challenging hypothetical reflection in the silicon realm of graphene, a one-atom thick graphite sheet, presently the hottest material in…
Applying the contact density chain-growth algorithm to lattice heteropolymers, we identify the conformational transitions of a nongrafted hydrophobic-polar heteropolymer with 103 residues in the vicinity of a polar, a hydrophobic, and a…
We initiate systematic study of EZ-structures (and associated boundaries) of groups acting on spaces that admit consistent and conical (equivalently, consistent and convex) geodesic bicombings. Such spaces recently drew a lot of attention…
The quantum cat map is a model for a quantum system with underlying chaotic dynamics. In this paper we study the matrix elements of smooth observables in this model, when taking arithmetic symmetries into account. We give explicit formulas…
We consider random walk on a mildly random environment on finite transitive d- regular graphs of increasing girth. After scaling and centering, the analytic spectrum of the transition matrix converges in distribution to a Gaussian noise. An…
Let $(\Sigma,p)$ be a pointed Riemann surface of genus $g\geq 1$. For any integer $k\geq 1$, we parametrize the space of meromorphic quadratic differentials on $\Sigma$ with a pole of order $(k+2)$ at $p$, having a connected critical graph…