Related papers: Construction Methods for Space-Filling Heterogeneo…
The success of topological insulators (TI) in creating devices with unique functionalities is directly connected to the ability of coupling their helical spin states to well defined perturbations. However, up to now, TI-based…
Porous structures are materials consisting of minuscule pores, where the microstructure morphology significantly impacts their macroscopic properties. Integrating different porous structures through a blending method is indispensable to…
Inspired by the quest for shape-shifting structures in a range of applications, we show how to create morphable structural materials using a neutrally stable unit cell as a building block. This unit cell is a self-stressed hinged structure…
This thesis establishes a generalised setting with which to unify the study of finite local complexity (FLC) patterns. The abstract notion of a "pattern" is introduced, which may be seen as an analogue of the space group of isometries…
The tenfold classification provides a powerful framework for organizing topological phases of matter based on symmetry and spatial dimension. However, it does not offer a systematic method for transitioning between classes or engineering…
The design of isophoric phased arrays composed of two-sized square-shaped tiles that fully cover rectangular apertures is dealt with. The number and the positions of the tiles within the array aperture are optimized to fit desired…
The study of interlocking assemblies is an emerging field with applications in various disciplines. However, to this day, the mathematical treatment of these assemblies has been sparse. In this work, we develop a comprehensive mathematical…
In typical topological insulator (TI) systems the TI is bordered by a non-TI insulator, and the surrounding conventional insulators, including vacuum, are not generally treated as part of the TI system. Here, we implement the first material…
The past decade has witnessed significant progress in topological materials investigation. Symmetry-indicator theory and topological quantum chemistry provide an efficient scheme to diagnose topological phases from only partial information…
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…
The design of irregular planar phased arrays (PAs) characterized by a highly-modular architecture is addressed. By exploiting the property of self-replicating tile shapes, also known as rep-tiles, the arising array layouts consist of tiles…
The Heesch problem 'grades' polygons that fail to tile the plane in terms of the number of layers (or corollas) of copies of it that can be formed around a central unit. We study the different topology of ' walls', which we define to be…
We present structures comprised of identical convex polyhedra which are interlocked geometrically. These sets cannot be disassembled by removing individual polyhedra by translations and/or rotations. The shapes that permit interlocking…
Tile-based self-assembly systems are capable of universal computation and algorithmically-directed growth. Systems capable of such behavior typically make use of "glue cooperation" in which the glues on at least $2$ sides of a tile must…
Van der Waals (vdW) heterostructures formed by 2D atomic crystals provide a powerful approach towards designer condensed matter systems. Incommensurate heterobilayers with small twisting and/or lattice mismatch lead to the interesting…
Recently, novel crystalline constructions known as Cayley-Schreier lattices have been suggested as a platform for realizing arbitrary gauge fields in synthetic crystals with real hopping amplitudes. We show that Cayley-Schreier lattices can…
This paper presents a density-based topology optimization method for designing 3D thin-walled structures with adaptive meshing. Uniform wall thickness is achieved by simultaneously constraining the minimum and maximum feature sizes using…
This paper introduces a new shape-matching methodology, combinative matching, to combine interlocking parts for geometric shape assembly. Previous methods for geometric assembly typically rely on aligning parts by finding identical surfaces…
We formulate topological crystalline materials on the basis of the twisted equivariant $K$-theory. Basic ideas of the twisted equivariant $K$-theory is explained with application to topological phases protected by crystalline symmetries in…
In this paper, we present a new approach to obtain symmetric tiles with curved edges. Our approach is based on using higher-order Voronoi sites that are closed under wallpaper symmetries. The resulting Voronoi tessellations provide us with…