Related papers: Totimorphic structures for space application
In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete…
Mechanical metamaterials are structures designed to exhibit an exotic response, such as topological soft modes at a surface. Here we explore single-material 3D prints of these topological structures by translating a ball-and-spring model…
In this paper, we apply transformation-based optics to the derivation of a general class of transparent metamaterial slabs. By means of analytical and numerical full-wave studies, we explore their image displacement/formation capabilities,…
How does one formalize the structure of structures necessary for the foundations of physics? This work is an attempt at conceptualizing the metaphysics of pregeometric structures, upon which new and existing notions of quantum geometry may…
Topological phase transitions, characterized by the closing and reopening of band gaps and a concomitant change in topological invariants, have played a central role in topological physics. However, such transitions have so far been…
Rapid advances in additive manufacturing over the past decade have kindled widespread interest in the rational design of metamaterials with unique properties. However, many applications require multi-physics metamaterials, where multiple…
We present a rational approach to the design of half-metallic heterostructures which allows the design of an infinite number of half-metallic heterostructures. The wide range of materials that can be made half-metallic using our approach…
The group of automorphisms of the geometry of an integrable system is considered. The geometrical structure used to obtain it is provided by a normal form representation of integrable systems that do not depend on any additional geometrical…
Plasmonics and metamaterials have attracted considerable attention over the past decade, owing to the revolutionary impacts that they bring to both the fundamental physics and practical applications in multiple disciplines. Although the two…
Within the framework of finite element systems, we show how spaces of differential forms may be constructed, in such a way that they are equipped with commuting interpolators and contain prescribed functions, and are minimal under these…
An emerging theme across many domains of science and engineering is materials that change shape, often dramatically. Determining their structure involves solving a shape optimization problem where a given energy functional is minimized with…
The topological mechanics is a perfect tool that can bridge the gap between the quantum and Newtonian physics and mechanics of materials. It requires discrete models of the material with analogies with the topological characteristics of…
First we introduce a generalization of symmetric spaces to parabolic geometries. We provide construction of such parabolic geometries starting with classical symmetric spaces and we show that all regular parabolic geometries with smooth…
Reprogrammable mechanical metamaterials, composed of a lattice of discretely adaptive elements, are emerging as a promising platform for mechanical intelligence. To operate in unknown environments, such structures must go beyond passive…
Metamaterials can enable peculiar static and dynamic behavior (such as negative effective mass density, dynamical stiffness, and Poisson's ratio) due to their geometry rather than their chemical composition. The geometry of these…
This article presents an overview of the theory of integrable systems with symmetries, focusing on toric systems, semitoric systems, and their classifications via decorated polygons. We discuss certain one-parameter families of integrable…
In contrast to the classical twistor spaces whose fibres are 2-spheres, we introduce twistor spaces over manifolds with almost quaternionic structures of the second kind in the sense of P. Libermann whose fibres are hyperbolic planes. We…
Metamaterials hold significant promise for enhancing the imaging capabilities of MRI machines as an additive technology, due to their unique ability to enhance local magnetic fields. However, despite their potential, the metamaterials…
This survey article describes the algorithmic approaches successfully used over the time to construct hyperbolic structures on 3-dimensional topological "objects" of various types, and to classify several classes of such objects using such…
Mechanical metamaterials owe their extraordinary properties and functionalities to their micro-/nanoscale design of which shape, including both geometry and topology, is perhaps the most important aspect. 4D printing enables programmed,…