Related papers: Asymptotic structure in substitution tiling spaces
In the present article we will give a new proof of the ground state asymptotics of the Dirichlet Laplacian with a Neumann window acting on functions which are defined on a two-dimensional infinite strip or a three-dimensional infinite…
Anderson and Putnam showed that the cohomology of a substitution tiling space may be computed by collaring tiles to obtain a substitution which "forces its border." One can then represent the tiling space as an inverse limit of an inflation…
We study asymptotics of the dimer model on large toric graphs. Let $\mathbb L$ be a weighted $\mathbb{Z}^2$-periodic planar graph, and let $\mathbb{Z}^2 E$ be a large-index sublattice of $\mathbb{Z}^2$. For $\mathbb L$ bipartite we show…
We provide an alternative characterization of two-dimensional locality (necessary e.g. to define the Hall conductivity of a Fermi projection) using the spectral projections of the Laughlin flux operator. Using this abstract…
Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary…
A topological defect separating a pair of two-dimensional CFTs is a codimension one interface along which all components of the stress-energy tensor glue continuously. We study topological defects of the bosonic, (0,1)- and…
Asymptotic formulae for the mechanical and electric fields in a piezoelectric body with a small void are derived and justified. Such results are new and useful for applications in the field of design of smart materials. In this way the…
We introduce a new general framework for constructing tilings of Euclidean space, which we call multiscale substitution tilings. These tilings are generated by substitution schemes on a finite set of prototiles, in which multiple distinct…
Existence, stability and dynamics of soliton complexes, centered at the site of a single transverse link connecting two parallel 2D (two-dimensional) lattices, are investigated. The system with the on-site cubic self-focusing nonlinearity…
We establish a local model for the moduli space of holomorphic symplectic structures with logarithmic poles, near the locus of structures whose polar divisor is normal crossings. In contrast to the case without poles, the moduli space is…
A new family of decagonal quasiperiodic tilings are constructed by the use of generalized point substitution processes, which is a new substitution formalism developed by the author [N. Fujita, Acta Cryst. A 65, 342 (2009)]. These tilings…
We study periodic tessellations of the Euclidean space with unequal cells arising from the minimization of perimeter functionals. Existence results and qualitative properties of minimizers are discussed for different classes of problems,…
In this paper, we use geometric tools to study the structure of asymptotic expanders and show that a sequence of asymptotic expanders always admits a "uniform exhaustion by expanders". It follows that asymptotic expanders cannot be coarsely…
It is known that every nonorientable surface $\Sigma$ has an orientable double cover $\tilde{\Sigma}$. The covering map induces an involution on the moduli space $\tilde{\M}$ of gauge equivalence classes of flat $G$-connections on…
In this paper we study the asymptotic behaviour via Gamma-convergence of some integral functionals which model some multi-dimensional structures and depend explicitly on the linearized strain tensor. The functionals are defined in…
In this note the result by A. Swift concerning the embeddability of countably branching bundle graphs into Banach spaces is extended from the context of reflexive spaces with an unconditional asymptotic structure to the context of dual…
We prove that is a measurable domain tiles R or R^2 by translations, and if it is "close enough" to a line segment or a square respectively, then it admits a lattice tiling. We also prove a similar result for spectral sets in dimension 1,…
We describe asymptotic symmetries at spatial infinity of asymptotically flat spacetimes within the context of a generalization of the Beig-Schmidt-Ashtekar-Romano-framework. We demonstrate that it is possible to relax certain smoothness…
We study spaces with directionally asymptotically controlled ellipsoids approximating the unit ball in finite-dimensions. These ellipsoids are the unique minimum volume ellipsoids, which contain the unit ball of the corresponding…
For a symplectic manifold with an anti-symplectic involution having non-empty fixed locus, we construct a model of the moduli space of real sphere maps out of moduli spaces of decorated disk maps and give an explicit expression for its…