Related papers: Optimal program-size complexity for self-assembly …
We use computational modeling to investigate the assembly thermodynamics of a particle-based model for geometrically frustrated assembly, in which the local packing geometry of subunits is incompatible with uniform, strain-free large-scale…
The field of algorithmic self-assembly is concerned with the design and analysis of self-assembly systems from a computational perspective, that is, from the perspective of mathematical problems whose study may give insight into the natural…
A lattice model with soft repulsion followed by attraction is developed for a monolayer of hybrid core-shell particles self-assembling at an interface. The model is solved exactly in one dimension. One, two or three periodic structures and…
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…
Self-organized complex structures in nature, e.g. viral capsids, hierarchical biopolymers, and bacterial flagella, offer efficiency, adaptability, robustness, and multi-functionality. Can we program the self-assembly of three-dimensional…
The rapid progress in precisely designing the surface decoration of patchy colloidal particles offers a new, yet unexperienced freedom to create building entities for larger, more complex structures in soft matter systems. However, it is…
The well-studied Two-Handed Tile Assembly Model (2HAM) is a model of tile assembly in which pairs of large assemblies can bind, or self-assemble, together. In order to bind, two assemblies must have matching glues that can simultaneously…
How hard is it to program $n$ robots to move about a long narrow aisle such that only $w$ of them can fit across the width of the aisle? In this paper, we answer that question by calculating the topological complexity of $\text{conf}(n,w)$,…
Silicon self-assembly at step edges in the initial stage of homoepitaxial growth on a vicinal Si(111) surface is studied by scanning tunneling microscopy (STM). The resulting atomic structures change dramatically from a parallel array of…
Algorithms for creating optimal configurations of warehouse threedimensional systems consisting of unified transport and warehouse modules are presented in the article. The constructions of these modules, and methods for constructing a…
The thermodynamics of the O(N) nonlinear sigma model in 1+1 dimensions is studied. We calculate the pressure to next-to-leading order in the 1/N expansion and show that at this order, only the minimum of the effective potential can be…
In this paper we show that passive self-assembly in the context of the tile self-assembly model is capable of performing fuel efficient, universal computation. The tile self-assembly model is a premiere model of self-assembly in which…
An $n$-dimensional chair consists of an $n$-dimensional box from which a smaller $n$-dimensional box is removed. A tiling of an $n$-dimensional chair has two nice applications in coding for write-once memories. The first one is in the…
In living cells, proteins self-assemble into large functional structures based on specific interactions between molecularly complex patches. Due to this complexity, protein self-assembly results from a competition between a large number of…
We investigate the problem of assembling general shapes and patterns in a model in which particles move based on uniform external forces until they encounter an obstacle. While previous work within this model of assembly has focused on…
We study the minimal complexity of tilings of a plane with a given tile set. We note that every tile set admits either no tiling or some tiling with O(n) Kolmogorov complexity of its n-by-n squares. We construct tile sets for which this…
In this paper, we investigate the abilities of systems of self-assembling tiles which can each pass a constant number of signals to their immediate neighbors to create replicas of input shapes. Namely, we work within the Signal-passing Tile…
Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and…
Interaction between dipolar forces, such as permanent magnets, generally leads to the formation of one-dimensional chains and rings. We investigated whether it was possible to let dipoles self-assemble into three-dimensional structures by…
The problem of rectangle tiling binary arrays is defined as follows. Given an $n \times n$ array $A$ of zeros and ones and a natural number $p$, our task is to partition $A$ into at most $p$ rectangular tiles, so that the maximal weight of…