Related papers: Wallpaper Groups and Auxetic Metamaterials
Crystallographic groups describe the symmetries of crystals and other repetitive structures encountered in nature and the sciences. These groups include the wallpaper and space groups. We derive linear and nonlinear representations of…
We consider invariant measures of maps on manifolds whose correlations decay at a sufficient rate and which satisfy a geometric contraction property. We then prove the that the limiting distribution of returns to geometric balls is…
The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which…
Lie groupoids and their associated algebroids arise naturally in the study of the constitutive properties of continuous media. Thus, Continuum Mechanics and Differential Geometry illuminate each other in a mutual entanglement of theory and…
The elastic properties of a material with spherical voids of equal volume are analysed using a new model, with particular attention paid to the hexagonal close-packed and the face-centred cubic arrangement of voids. Void fractions well…
We develop further Cannon's method of cone types for finding the growth function of a group, which can also be used to find the coordination sequences of certain infinite graphs. We then apply this method to compute the growth functions and…
The graphene-graphite relationship in structural geometry is a basic principle to predict novel two-dimensional (2D) materials. Here, we demonstrate that this is not the case in binary metallic systems. We use the Bayesian optimization…
A Poisson system is a Poisson point process and a group action, together forming a measure-preserving dynamical system. Ornstein and Weiss proved Poisson systems over many amenable groups were isomorphic in their 1987 paper. We consider…
The paper studies the modes of vibrations of a lattice with rod-like particles, in a continuum model where the sites of the lattice are the connections among strings and rigid rods. In these structures then, translational and rotational…
The problem of obtaining anisotropic auxetic composite laminates, i.e. having a negative Poisson's ratio for at least some directions, is examined in this paper. In particular, the possibility of obtaining auxeticity stacking…
Thin elastic sheets and membranes are known to wrinkle when they are stretched -- the associated physics is highly non-linear. The mechanics of thin films that exhibit unusual behavior upon stretching, when they possess auxetic structure,…
We define algebras of admissible functions associated to twisted Dirac structures, and we show that they are Poisson algebras. We study the standard cases associated to Dirac structures defined by graphs of non-degenerate 2-forms.
One of the basic aims of this paper is to study the relationship between the geometry of ``hypersurface like'' subsets of Euclidean space and the properties of the measures they support. In this context we show that certain doubling…
In this paper, we study invariant Poisson structures on homogeneous manifolds, which serve as a natural generalization of homogeneous symplectic manifolds previously explored in the literature. Our work begins by providing an algebraic…
Current research on three-dimensional metamaterial has largely focused on conventional strut, plate, and shell-based lattice designs. Although these designs offer several advantages, they possess inherent limitations that can restrict their…
We perform molecular dynamics simulations to investigate the effect of hydrogenation on the Poisson's ratio of graphene. It is found that the value for Poisson's ratio in graphene can be effectively tuned from positive to negative by…
In recent years, there has been a notable increase in the significance of active mechanical metamaterials capable of being remotely manipulated through changes in external stimuli. While research in this area has achieved considerable…
Recent theoretical studies of chaotic scattering have encounted ensembles of random matrices in which the eigenvalue probability density function contains a one-body factor with an exponent proportional to the number of eigenvalues. Two…
In this paper, we study staircase tableaux, a combinatorial object introduced due to its connections with the asymmetric exclusion process (ASEP) and Askey-Wilson polynomials. Due to their interesting connections, staircase tableaux have…
The Gleason groups serve as the primary histological grading system for prostate cancer, providing crucial insights into the cancer's potential for growth and metastasis. In clinical practice, pathologists determine the Gleason groups based…