Related papers: Strict Self-Assembly of Discrete Sierpinski Triang…

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…

This paper provides a bridge between the classical tiling theory and the complex neighborhood self-assembling situations that exist in practice. The neighborhood of a position in the plane is the set of coordinates which are considered…

We introduce a new property of tile self-assembly systems that we call size-separability. A system is size-separable if every terminal assembly is a constant factor larger than any intermediate assembly. Size-separability is motivated by…

If particles interact according to isotropic pair potentials that favor multiple length scales, in principle a large variety of different complex structures can be achieved by self-assembly. We present, motivate, and discuss a conjecture…

Optimal Morse matchings reveal essential structures of cell complexes which lead to powerful tools to study discrete geometrical objects, in particular discrete 3-manifolds. However, such matchings are known to be NP-hard to compute on…

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…

We introduce a new DNA tile self-assembly model: the Surface Flexible Tile Assembly Model (SFTAM), where 2D tiles are placed on host 3D surfaces made of axis-parallel unit cubes glued together by their faces, called polycubes. The bonds are…

Discrete conformal mappings based on circle packing, vertex scaling, and related structures has had significant activity since Thurston proposed circle packing as a way to approximate conformal maps in the 1980s. The first convergence…

In this work we propose a generalization of Winfree's abstract Tile Assembly Model (aTAM) in which tile types are assigned rigid shapes, or geometries, along each tile face. We examine the number of distinct tile types needed to assemble…

One of the challenges of self-assembling finite-sized colloidal aggregates with a sought morphology is the necessity of precisely sorting the position of the colloids at the microscopic scale to avoid the formation of off-target structures.…

Sequence-directed assembly processes - such as protein folding - allow the assembly of a large number of structures with high accuracy from only a small handful of fundamental building blocks. We aim to explore how efficiently sequence…

The Abelian Sandpile Model, seen as a deterministic lattice automaton, on two-dimensional periodic graphs generates complex regular patterns displaying (fractal) self-similarity. In particular, on a variety of lattices and initial…

Self-assembly is a fundamental process by which supramolecular species form spontaneously from their components. This process is ubiquitous throughout the life chemistry and is central to biological information processing. Algorithms for…

Highly periodic structures are often said to convey the beauty of nature. However, most material properties are strongly influenced by the defects they contain. On the mesoscopic scale, molecular self-assembly exemplifies this interplay;…

We present a mechanism and show two variants of a method where the average diameter of spontaneously (barrier-free) assembled single component unilamellar liposomes is intrinsic, in agreement with Helfrich's theory. It depends only on the…

The identification of repeating patterns in discrete grids is rudimentary within symbolic reasoning, algorithm synthesis and structural optimization across diverse computational domains. Although statistical approaches targeting noisy data…

We construct symmetric self-similar Dirichlet forms on unconstrained Sierpinski carpets, which are natural extension of planar Sierpinski carpets by allowing the small cells to live off the $1/k$ grids. The intersection of two cells can be…

The Pattern self-Assembly Tile set Synthesis (PATS) problem, which arises in the theory of structured DNA self-assembly, is to determine a set of coloured tiles that, starting from a bordering seed structure, self-assembles to a given…

Discrete rearranging patterns include cellular patterns, for instance liquid foams, biological tissues, grains in polycrystals; assemblies of particles such as beads, granular materials, colloids, molecules, atoms; and interconnected…

Self-assembly of granular particles is of great interest in both applied and basic research. It is commonly observed that when randomly packed into a container, granular particles form disordered structures like glass. As the particles are…