Related papers: Size-Separable Tile Self-Assembly: A Tight Bound f…
Multifarious assembly models consider multiple structures assembled from a shared set of components, reflecting the efficient usage of components in biological self-assembly. These models are subject to a high-dimensional parameter space,…
We introduce TexTile, a novel differentiable metric to quantify the degree upon which a texture image can be concatenated with itself without introducing repeating artifacts (i.e., the tileability). Existing methods for tileable texture…
The process of self-assembly is guided by the minimization of free energy, which limits the symmetries available for assembly and ultimately the usefulness of devices fabricated in this fashion. Here, we demonstrate experimentally for the…
The hallmark feature of polymorphic systems is their ability to assemble into many possible structures at the same thermodynamic state. Designer polymorphic materials can in principle be engineered via programmable self-assembly, but the…
In this paper we propose a research programme for getting structural characterisations for 2-dimensional languages generated by self-assembling tiles. This is part of a larger programme on getting a formal foundation of parallel,…
Patterned self-assembly tile set synthesis PATS is the problem of finding a minimal tile set which uniquely self-assembles into a given pattern. Czeizler and Popa proved the NP-completeness of PATS and Seki showed that the PATS problem is…
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…
Perhaps the two most significant theoretical questions about the programming of self-assembling agents are: (1) necessary and sufficient conditions to produce a unique terminal assembly, and (2) error correction. We address both questions,…
We present algorithmic results for the parallel assembly of many micro-scale objects in two and three dimensions from tiny particles, which has been proposed in the context of programmable matter and self-assembly for building high-yield…
The Pattern self-Assembly Tile set Synthesis (PATS) problem is to determine a set of coloured tiles that self-assemble to implement a given rectangular colour pattern. We give an exhaustive branch-and-bound algorithm to find tile sets of…
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…
Both biological and artificial self-assembly processes can take place by a range of different schemes, from the successive addition of identical building blocks, to hierarchical sequences of intermediates, all the way to the fully…
Controlled micro- to meso-scale porosity is a common materials design goal with possible applications ranging from molecular gas adsorption to particle size selective permeability or solubility. Here, we use inverse methods of statistical…
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…
We show here that a model called directed self-assembly at temperature 1 is unable to do complex computations like the ones of a Turing machine. Since this model can be seen as a generalization of finite automata to 2D languages, a logical…
Equilibrium states of infinite extended lattice systems at high temperature are studied with respect to their entanglement. Two notions of separability are offered. They coincide for finite systems but differ for infinitely extended ones.…
The fluid phase diagram of trimer particles composed of one central attractive bead and two repulsive beads was determined as a function of simple geometric parameters using flat-histogram Monte Carlo methods. A variety of self-assembled…
Rational design strategies for self-assembly require a detailed understanding of both the equilibrium state and the assembly kinetics. While the former is starting to be well understood, the latter remains a major theoretical challenge,…
Thermal rectification is of importance not only for fundamental physics, but also for potential applications in thermal manipulations and thermal management. However, thermal rectification effect usually decays rapidly with system size.…
We show that finite size scaling techniques can be employed to study the glass transition. Our results follow from the postulate of a diverging correlation length at the glass transition whose physical manifestation is the presence of…