Related papers: Self-Assembly of Discrete Self-Similar Fractals
Quasicrystals are fascinating structures, characterized by strong positional order but lacking the periodicity of a crystal. In colloidal systems, quasicrystals are typically predicted for particles with complex or highly specific…
In this paper, we propose a new approach -- the Tempered Finite Element Method (TFEM) -- that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM…
We have studied high temperature thermal behavior of 1H, 1H, 2H, 2H-Perfluorooctyl-trichlorosilane (FOTS) and Octyltrichlorosilane (OTS) molecules self assembled on titanium dioxide (TiO2) nanoparticles using advanced microscopy and…
We characterize the existence of certain geometric configurations in the fractal percolation limit set $A$ in terms of the almost sure dimension of $A$. Some examples of the configurations we study are: homothetic copies of finite sets,…
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…
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…
We show that geometric frustration in a broad class of deformable and naturally curved, shell-like colloidal particles gives rise to self-limiting assembly of finite-sized stacks that far exceed particle dimensions. When inter-particle…
Context. A porous and/or fractal description can generally be applied where particles have undergone coagulation into aggregates. Aims. To characterise finite-sized, porous and fractal particles and to understand the possible limitations of…
We establish asymptotics of growing one dimensional self-similar fractal graphs, they are networks that allow multiple weighted edges between nodes, in terms of quantum central limit theorems for algebraic probability spaces in pure state.…
We present an active tile assembly model which extends Winfree's abstract tile assembly model to tiles that are capable of transmitting and receiving binding site activation signals. In addition, we introduce a mathematical framework to…
The self-assembly of nanocrystals enables new classes of materials whose properties are controlled by the periodicities of the assembly, as well as by the size, shape and composition of the nanocrystals. While self-assembly of spherical…
Understanding the relationship between colloidal building block shape and self-assembled material structure is important for the development of novel materials by self-assembly. In this regard, colloidal superballs are unique building…
Controlling the topology of structures self-assembled from a set of heterogeneous building blocks is highly desirable for many applications, but is poorly understood theoretically. Here we show that the thermodynamic theory of self-assembly…
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
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…
We study an extreme scenario of the Mastrand projection theorem for which a fractal has the property that its orthogonal projection is the same as the orthogonal projection of its convex hull. We extend results in current literature and…
We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing conditions which are governed the relation between the…
Controlling the self-assembly of supramolecular structures is vital for living cells, and a central challenge for engineering at the nano- and microscales. Nevertheless, even particles without optimized shapes can robustly form well-defined…
We develop an algorithm to construct new self-similar space-filling packings of spheres. Each topologically different configuration is characterized by its own fractal dimension. We also find the first bi-cromatic packing known up to now.
The efficient and controlled assembly of complex structures from macromolecular building blocks is a critical open question in both biological systems and nanoscience. Using molecular dynamics simulations we study the self-assembly of…