Related papers: Strict Self-Assembly of Discrete Self-Similar Frac…
In this paper, we investigate shape-assembling power of a tile-based model of self-assembly called the Signal-Passing Tile Assembly Model (STAM). In this model, the glues that bind tiles together can be turned on and off by the binding…
Tile assembly systems in the abstract Tile Assembly Model (aTAM) are computationally universal and capable of building complex shapes, but DNA-based implementations encounter formidable error rates that stifle this theoretical potential.…
Self-assembly is one of the prevalent strategies used by living systems to fabricate ensembles of precision nanometer-scale structures and devices. The push for analogous approaches to create synthetic nanomaterials has led to the…
We prove that the abstract Tile Assembly Model (aTAM) of nanoscale self-assembly is intrinsically universal. This means that there is a single tile assembly system U that, with proper initialization, simulates any tile assembly system T.…
Self-assembly is the autonomous organization of components into patterns or structures: an essential ingredient of biology and a desired route to complex organization. At equilibrium, the structure is encoded through specific interactions,…
We define the Reflexive Tile Assembly Model (RTAM), which is obtained from the abstract Tile Assembly Model (aTAM) by allowing tiles to reflect across their horizontal and/or vertical axes. We show that the class of directed temperature-1…
The method of spectral decimation is applied to an infinite collection of self--similar fractals. The sets considered belong to the class of nested fractals, and are thus very symmetric. An explicit construction is given to obtain formulas…
The goal of inverse self-assembly is to design inter-particle interactions capable of assembling the units into a desired target structure. The effective assembly of complex structures often requires the use of multiple components, each new…
In this paper we explore the power of tile self-assembly models that extend the well-studied abstract Tile Assembly Model (aTAM) by permitting tiles of shapes beyond unit squares. Our main result shows the surprising fact that any aTAM…
Self-assembly is the mechanism that controls the formation of well defined structures from disordered pre-existing parts. Despite the importance of self-assembly as a manufacturing method and the increasingly large number of experimental…
In this paper we present a model containing modifications to the Signal-passing Tile Assembly Model (STAM), a tile-based self-assembly model whose tiles are capable of activating and deactivating glues based on the binding of other glues.…
Experiments have reached a monumental capacity for designing and synthesizing microscopic particles for self-assembly, making it possible to precisely control particle concentrations, shapes, and interactions. However, more physical insight…
Self-assembly of complex and functional materials remains a grand challenge in soft material science. Efficient assembly depends on a delicate balance between thermodynamic and kinetic effects, requiring fine-tuning affinities and…
For self-similar fractals, the Minkowski content and fractal curvature have been introduced as a suitable limit of the geometric characteristics of its parallel sets, i.e., of uniformly thin coatings of the fractal. For some self-conformal…
Algorithmic self-assembly occurs when disorganized components autonomously combine to form structures and, by their design and the dynamics of the system, are forced to follow the execution of algorithms. Motivated by applications in…
A self-organization is an universal phenomenon in nature and, in particular, is highly important in materials systems and biology. We proposed a new theory that allowed us to model the most challenging cases of atomic self-assembling whose…
In this paper, we introduce the following problem in the theory of algorithmic self-assembly: given an input shape as the seed of a tile-based self-assembly system, design a finite tile set that can, in some sense, uniquely identify whether…
In this paper, we work in a 2D version of the probabilistic variant of Winfree's abstract Tile Assembly Model defined by Chandran, Gopalkrishnan and Reif (SICOMP 2012) in which attaching tiles are sampled uniformly with replacement. First,…
Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral…
The Sierpinski Triangle (ST) is a fractal mathematical structure that has been used to explore the emergence of flat bands in lattices of different geometries and dimensions in condensed matter. Here we look into fractal features in the…