Related papers: A pumping lemma for non-cooperative self-assembly
We consider methods for connected reconfigurations by finite automate in the so-called \emph{hybrid} or \emph{Robot-on-Tiles} model of programmable matter, in which a number of simple robots move on and rearrange an arrangement of passive…
Particle-particle interaction provides a new degree of freedom to induce novel topological phenomena. Here, we propose to use spatiotemporal modulation of interaction to realize topological pumping without single-particle counterpart.…
A particular, two-dimensional, tiling model, composed by the so called Wang tiles has been studied at finite temperature by Monte Carlo numerical simulations. In absence of any thermal bath the Wang tiles give the opportunity of building a…
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…
We consider tiles (dimers) each of which covers two vertices of a rectangular lattice. There is a normalized translation invariant weighting on the shape of the tiles. We study the pressure, p, or entropy, (one over the volume times the…
We prove that by successively combining subassemblies, we can achieve sublinear construction times for "staged" assembly of micro-scale objects from a large number of tiny particles, for vast classes of shapes; this is a significant advance…
We present fast simulation methods for the self-assembly of complex shapes in two dimensions. The shapes are modeled via a general boundary curve and interact via a standard volume term promoting overlap and an interpenetration penalty. To…
One emerging approach for the fabrication of complex architectures on the nanoscale is to utilize particles customized to intrinsically self-assemble into a desired structure. Inverse methods of statistical mechanics have proven…
Synthetic nanoscale complexes capable of mechanical movement are often studied theoretically using discrete-state models that involve instantaneous transitions between metastable states. A number of general results have been derived within…
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…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
This paper discusses the design and implementation of the Modular Pipe Climber inside ASTM D1785 - 15e1 standard pipes [1]. The robot has three tracks which operate independently and are mounted on three modules which are oriented at…
We study the behaviour at tipping points close to (smoothed) non-smooth fold bifurcations in one-dimensional oscillatory forced systems. The focus is the Stommel-Box, and related climate models, which are piecewise-smooth continuous…
Microfluidics involves the manipulation of flows at the microscale, typically requiring external power sources to generate pressure gradients. Alternatively, harnessing flows from active fluids, which are usually chaotic, has been proposed…
Stripe patterns are ubiquitous in nature and everyday life. While the synthesis of these patterns has been thoroughly studied in the literature, their potential to control the mechanics of structured materials remains largely unexplored. In…
Building structures with hierarchical order through the self-assembly of smaller blocks is not only a prerogative of nature, but also a strategy to design artificial materials with tailored functions. We explore in simulation the…
We study the computational power of the Full-Tilt model of motion planning, where slidable polyominos are moved maximally around a board by way of a sequence of directional ``tilts.'' We focus on the deterministic scenario in which the…
A major goal in nanoscience and nanotechnology is the self-assembly of any desired complex structure with a system of particles interacting through simple potentials. To achieve this objective, intense experimental and theoretical efforts…
Molecular-scale computation is crucial for smart materials and nanoscale devices, yet creating single-molecule systems capable of complex computations remains challenging. We present a theoretical framework for a single-molecule computer…
Self-assembly, the process by which interacting components form well-defined and often intricate structures, is typically thought of as a spontaneous process arising from equilibrium dynamics. When a system is driven by external…