Related papers: Self-Assembly of Patterns in the abstract Tile Ass…
In 2004, Klavins et al. introduced the use of graph grammars to describe -- and to program -- systems of self-assembly. We show that these graph grammars can be embedded in a graph rewriting characterization of distributed systems that was…
Mutually repelling particles form spontaneously ordered clusters when forced into confinement. The clusters may adopt similar spatial arrangements even if the underlying particle interactions are contrastingly different. Here we demonstrate…
We use numerical simulations to show how noninteracting hard particles binding to a deformable elastic shell may self-assemble into a variety of linear patterns. This is a result of the nontrivial elastic response to deformations of shells.…
External control of the swimming speed of `active particles' can be used to self assemble designer structures in situ on the micrometer to millimeter scale. We demonstrate such reconfigurable templated active self assembly in a fluid…
Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…
The generation of nanoscale square and stripe patterns is of major technological importance since they are compatible with industry-standard electronic circuitry. Recently, a blend of diblock copolymer interacting via hydrogen-bonding was…
Control over the physical properties of materials is ubiquitously required in many fields. One means by which this can be achieved is controlling the internal structure of multi-component materials with an eye to enhancing mechanical…
Experiments have reached a monumental capacity for designing and synthesizing microscopic particles for self-assembly, making it possible to precisely control particle concentrations, shapes, and interactions. However, more physical insight…
We are entering a new era in which software systems are becoming more and more complex and larger. So, the composition of such systems is becoming infeasible by manual means. To address this challenge, self-organising software models…
Self-assembly is traditionally described as the process through which an initially disordered system relaxes towards an equilibrium ordered phase only driven by local interactions between its building blocks. However, This definition is too…
Tilings of the plane resemble the simplicial and other complexes from algebraic topology, but have not been studied from this perspective. We construct finite categories corresponding to polygons with labeled directed edges, and introduce…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
At the cutting edge of materials science, matter is designed to self-organize into structures that perform a wide range of functions. The past two decades have witnessed major innovations in the versatility of building blocks, ranging from…
The Generalized Sliding-Tile Puzzle (GSTP), allowing many square tiles on a board to move in parallel while enforcing natural geometric collision constraints on the movement of neighboring tiles, provide a high-fidelity mathematical model…
In this short note we construct two families of examples of large stratifying systems in module categories of algebras. The first examples consists on stratifying systems of infinite size in the module category of an algebra $A$. In the…
A combinatorial tiling of the sphere is naturally given by an embedded graph. We study the case that each tile has exactly five edges, with the ultimate goal of classifying combinatorial tilings of the sphere by geometrically congruent…
We show that given any tiling of Euclidean space, any geometric patterns of points, we can find a patch of tiles (of arbitrarily large size) so that copies of this patch appear in the tiling nearly centered on a scaled and translated…
Discrete tomography deals with reconstructing finite spatial objects from lower dimensional projections and has applications for example in timetable design. In this paper we consider the problem of reconstructing a tile packing from its…
We propose a formalism for tilings with infinite local complexity (ILC), and especially fusion tilings with ILC. We allow an infinite variety of tile types but require that the space of possible tile types be compact. Examples include…
The regular polyhedra have the highest order of 3D symmetries and are exceptionally at- tractive templates for (self)-assembly using minimal types of building blocks, from nano-cages and virus capsids to large scale constructions like glass…