Related papers: Wallpaper Groups and Auxetic Metamaterials
The ability to change a surface's profile allows biological systems to effectively manipulate and blend into their surroundings. Current surface morphing techniques rely either on having a small number of fixed states or on directly driving…
In this paper, we study formal deformations of Poisson structures, especially for three families of Poisson varieties in dimensions two and three. For these families of Poisson structures, using an explicit basis of the second Poisson…
The nine two-dimensional Cayley-Klein geometries are firstly reviewed by following a graded contraction approach. Each geometry is considered as a set of three symmetrical homogeneous spaces (of points and two kinds of lines), in such a…
In materials science, auxetic behavior refers to lateral widening upon stretching. We investigate the problem of finding domains of auxeticity in global deformation spaces of periodic frameworks. Case studies include planar periodic…
The purpose of this paper is to propose a version of the notion of convenient Lie groupoid as a generalization of this concept in finite dimension. The authors point out which obstructions appear in the infinite dimensional context and how…
We give functorial recipes to get, out of any Hopf algebra over a field, two pairs of Hopf algebras which have some geometrical content. When the ground field has characteristic zero, the first pair is made by a function algebra over a…
Poisson distributed measurements in inverse problems often stem from Poisson point processes that are observed through discretized or finite-resolution detectors, one of the most prominent examples being positron emission tomography (PET).…
Local patterns play an important role in statistical physics as well as in image processing. Two-dimensional ordinal patterns were studied by Ribeiro et al. who determined permutation entropy and complexity in order to classify paintings…
We develop the deformation theory of symplectic foliations, i.e. regular foliations equipped with a leafwise symplectic form. The main result of this paper is that each symplectic foliation has an attached $L_\infty$-algebra controlling its…
We revise the Bayesian inference steps required to analyse the cosmological large-scale structure. Here we make special emphasis in the complications which arise due to the non-Gaussian character of the galaxy and matter distribution. In…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
Groupoids are mathematical structures able to describe symmetry properties more general than those described by groups. They were introduced (and named) by H. Brandt in 1926. Around 1950, Charles Ehresmann used groupoids with additional…
The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios…
In the context of averaging method, we describe a reconstruction of invariant connection-dependent Poisson structures from canonical actions of compact Lie groups on fibered phase spaces. Some symmetry properties of Wong's type equations…
We consider two random group models: the hexagonal model and the square model, defined as the quotient of a free group by a random set of reduced words of length four and six respectively. Our first main result is that in this model there…
We leverage quantum graph theory to quickly and accurately characterise acoustic metamaterials comprising networks of interconnected pipes. Anisotropic bond lengths are incorporated in the model that correspond to space-coiled acoustic…
We describe a deformation quantization of a modification of Poisson geometry by a closed 3-form. Under suitable conditions it gives rise to a stack of algebras. The basic object used for this aim is a kind of families of Poisson structures…
The use of metamaterial as a way to mitigate the negative effects of absorption in metals on the Purcell effect in metal-dielectric structures is investigated. A layered metal-dielectric structure is considered as an anisotropic medium in…
It is shown in this paper how a connection may be made between the symmetry generators of the Hamiltonian (or potential) invariant under a symmetry group $G$, and the subcasimirs that come about when the rank of the Poisson structure of a…
Geometric compatibility constraints dictate the mechanical response of soft systems that can be utilized for the design of mechanical metamaterials such as the negative Poisson ratio Miura-ori origami crease pattern. Here, we develop a…