Related papers: DNA tile self-assembly for 3D-surfaces: Towards ge…
We ask the question of how small a self-assembling set of tiles can be yet have interesting computational behaviour. We study this question in a model where supporting walls are provided as an input structure for tiles to grow along: we…
We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are…
Molecular self-assembly is a well-known technique to create highly functional nanostructures on surfaces. Self-assembly on two-dimensional materials is a developing field and has already resulted in the discovery of several rich and…
In this paper, we prove that in the abstract Tile Assembly Model (aTAM), an accretion-based model which only allows for a single tile to attach to a growing assembly at each step, there are no tile assembly systems capable of…
The algorithmic self-assembly of shapes has been considered in several models of self-assembly. For the problem of \emph{shape construction}, we consider an extended version of the Two-Handed Tile Assembly Model (2HAM), which contains…
In equilibrium self-assembly, microscopic building blocks spontaneously self-organize into stable structures as dictated by their interaction potentials, which limits the accessible structural features to those that correspond to global…
The ability to design and synthesize ever more complicated colloidal particles opens the possibility of self-assembling a zoo of complex structures, including those with one or more self-limited length scales. An undesirable feature of…
Patchy colloids are promising candidates for building blocks in directed self-assembly. To be successful the surface patterns need to both be simple enough to be synthesized, while feature-rich enough to cause the colloids to self-assemble…
Self-assembly is a phenomenon observed in nature at all scales where autonomous entities build complex structures, without external influences nor centralised master plan. Modelling such entities and programming correct interactions among…
We present a strict separation between the class of "mismatch free" self-assembly systems and general aTAM systems. Mismatch free systems are those systems in which concurrently grown parts must always agree with each other. Tile…
Engineering shape and interactions of nanoscopic building blocks allows for the assembly of rationally designed macroscopic three-dimensional (3D) materials with spatial accuracy inaccessible to top-down fabrication methods. Owing to its…
Surface plasmon resonances generated in metallic nanostructures can be utilized to tailor electromagnetic fields. The precise spatial arrangement of such structures can result in surprising optical properties that are not found in any…
We present a modular DNA origami design approach to address the challenges of assembling geometrically complex nanoscale structures, including those with nonuniform Gaussian curvature. This approach features a core structure that completely…
This paper introduces a method to generate highly selective encodings that can be magnetically "programmed" onto physical modules to enable them to self-assemble in chosen configurations. We generate these encodings based on Hadamard…
Winfree (1998) showed that discrete Sierpinski triangles can self-assemble in the Tile Assembly Model. A striking molecular realization of this self-assembly, using DNA tiles a few nanometers long and verifying the results by atomic-force…
We study the structure of the digit sets ${\mathcal D}$ for the integral self-similar tiles $T(b,{\mathcal{D}})$ (we call such ${\mathcal D}$ a {\it tile digit set} with respect to $b$). So far the only available classes of such tile digit…
By exploiting the exquisite selectivity of DNA hybridization, DNA-Coated Colloids (DNACCs) can be made to self-assemble in a wide variety of structures. The beauty of this system stems largely from its exceptional versatility and from the…
We discuss the self-assembly system of triangular tiles instead of square tiles, in particular right triangular tiles and equilateral triangular tiles. We show that the triangular tile assembly system, either deterministic or…
Biology is full of intricate molecular structures whose geometries are inextricably linked to their function. Many of these structures exhibit varying curvature, such as the helical structure of the bacterial flagellum, which is critical…
In contrast to most self-assembling synthetic materials, which undergo unbounded growth, many biological self-assembly processes are self-limited. That is, the assembled structures have one or more finite dimensions that are much larger…