Related papers: New principles for auxetic periodic design
We present an adaptation of a relatively simple topological argument to show the existence of many periodic orbits in an infinite dimensional dynamical system, provided that the system is close to a one-dimensional map in a certain sense.…
We present a complete suite of algorithms for finding isotropic vectors of quadratic forms (of any dimension) over an arbitrary global field of characteristic different from 2. This is a new version with numerous changes and improvements.
The structural complexity of metamaterials is limitless, although in practice, most designs comprise periodic architectures which lead to materials with spatially homogeneous features. More advanced tasks, arising in e.g. soft robotics,…
In this paper the authors find examples of translation surfaces that have infinitely generated Veech groups, satisfy the topological dichotomy property that for every direction either the flow in that direction is completely periodic or…
We construct infinite periodic versions of the stress matrix and establish sufficient conditions for periodic tensegrity frameworks to be globally rigid in $\mathbb{R}^d$ in the cases when the lattice is either fixed, fully flexible, or…
We find an infinite number of noncommutative geometries which posses a differential structure. They generalize the two dimensional noncommutative plane, and have infinite dimensional representations. Upon applying generalized coherent…
We prove that a set of finite perimeter is indecomposable if and only if it is, up to a choice of suitable representative, connected in the 1-fine topology. This gives a topological characterization of indecomposability which is new even in…
In this paper the notion of Dirac structure in finite dimension is extended to the convenient setting. In particular, we introduce the notion of partial Dirac structure on convenient Lie algebroids and manifolds. We then look for those…
Within periodic materials and structures, wave scattering and dispersion occur across constituent material interfaces leading to a banded frequency response. In an earlier paper, the elastodynamics of one-dimensional periodic materials and…
We require decomposition methods for the ABCD-matrix formulation in rotationally symmetric paraxial geometric optics when designing a multi-component optical system from a given single paraxial specification (represented by an ABCD matrix)…
We prove the existence of small amplitude periodic solutions, for a large Lebesgue measure set of frequencies, in the nonlinear beam equation with a weak quadratic and velocity dependent nonlinearity and with Dirichlet boundary conditions.…
This paper proposes an efficient FDTD technique for determining electromagnetic fields interacting with a finite-sized 2D and 3D periodic structures. The technique combines periodic boundary conditions---modelling fields away from the edges…
We classify all spherical 2-designs that arise as orbits of finite group actions on real inner product spaces. Although it is well known that such designs can occur in representations without trivial components, we give a complete…
It is proved that the set of geodesic circles in two dimensions may be given a variational description and the explicit form of it is presented. In the limit case of the Euclidean geometry a certain claim of uniqueness of such description…
In this paper we study the kaleidoscopic pseudo-randomness of finite Euclidean graphs using probabilistic methods. Roughly speaking, we show that sufficiently large subsets of d-dimensional vector spaces over finite fields contain every…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
A new sequential approach to investigations of structure of metric spaces at infinity is proposed. Criteria for finiteness and boundedness of metric spaces at infinity are found.
In this paper, we present a general theory of aperiodic subwavelength arrays for controlling electromagnetic waves. The considered platform is formed by an array of electrically small loaded scatterers above a ground plane. While the array…
We construct a countable family of multi-dimensional continued fraction algorithms, built out of five specific multidimensional continued fractions, and find a wide class of cubic irrational real numbers a so that either (a, a^2) or (a,…
Skeletal polyhedra and polygonal complexes are finite or infinite periodic structures in 3-space with interesting geometric, combinatorial, and algebraic properties. These structures can be viewed as finite or infinite periodic graphs…