Related papers: Construction Methods for Space-Filling Heterogeneo…
This work presents a construction method for interlocking assemblies based on planar crystallographic symmetries. Planar crystallographic groups, also known as wallpaper groups, correspond to tessellations of the plane with a tile, called a…
Topological interlocking assemblies (TIA) are arrangements of blocks such that rigid-body motions of the blocks are fully constrained by their neighbours and a fixed frame. In this work, we investigate tubular interlocking structures…
A topological interlocking assembly consists of rigid blocks together with a fixed frame, such that any subset of blocks is kinematically constrained and therefore cannot be removed from the assembly. In this paper we pursue a modular…
Topological Interlocking assemblies are arrangements of blocks kinematically constrained by a fixed frame, such that all rigid body motions of each block are constrained only by its permanent contact with other blocks and the frame. In the…
Topologically interlocked material systems are two-dimensional assemblies of unit elements from which no element can be removed from the assembly without disassembly of the entire system. Consequently, such tile assemblies are able to carry…
A topological interlocking assembly is an arrangement of blocks, where all blocks are kinematically constrained by their neighboring blocks and a fixed frame. This concept has been known for a long time, attracting recent interest due to…
In this paper, we present an algorithmic approach to design and construct planar truss structures based on symmetric lattices using modular elements. The method of assembly is similar to Leonardo grids as they both rely on the property of…
Topologically interlocked materials and structures, which are assemblies of unbonded interlocking building blocks, are promising concepts for versatile structural applications. They have been shown to exhibit exceptional mechanical…
Topological Interlocking Structures (TIS) are assemblies of interlocking building blocks that hold together solely through contact and friction at the blocks' interfaces, and thus do not require any connective elements. This salient feature…
In the abstract Tile Assembly Model, self-assembling systems consisting of tiles of different colors can form structures on which colored patterns are ``painted.'' We explore the complexity, in terms of the numbers of unique tile types…
In this note we use techniques in the topology of 2-complexes to recast some tools that have arisen in the study of planar tiling questions. With spherical pictures we show that the tile counting group associated to a set $T$ of tiles and a…
Self-assembled monolayers of microparticles encoding Archimedean and non-regular tessellations promise unprecedented structure-property relationships for a wide spectrum of applications in fields ranging from optoelectronics to surface…
Topologically interlocked structures are assemblies of interlocking blocks that hold together solely through contact. Such structures have been shown to exhibit high strength, energy dissipation, and crack arrest properties. Recent studies…
The number of distinguishable inherent structures of a liquid is the key component to understanding the thermodynamics of glass formers. In the case of hard potential systems such as hard discs, spheres and ellipsoids, an inherent structure…
To understand an aperiodic tiling (or a quasicrystal modeled on an aperiodic tiling), we construct a space of similar tilings, on which the group of translations acts naturally. This space is then an (abstract) dynamical system. Dynamical…
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…
It is well known that if there exists a finite set of convex bodies on the plane with non-overlapping interiors, then there is at least one "extremal" one among them, i.e., some one which can be continuously "taken away to the infinity"…
A basic assumption of tiling theory is that adjacent tiles can meet in only a finite number of ways, up to rigid motions. However, there are many interesting tiling spaces that do not have this property. They have "fault lines", along which…
We present a unified framework to construct and classify topological crystalline superconductors (TCSCs). The building blocks are one-dimensional topological superconductors (TSCs) protected solely by onsite symmetries, which are arranged…
Topologically Interlocked Structures (TIS) are structural assemblies that achieve stability and carrying capacity through the geometric arrangement of interlocking blocks, relying solely on normal and friction forces for load transfer.…