Related papers: Scaled tree fractals do not strictly self-assemble
We prove that if a set $X \subseteq \Z^2$ weakly self-assembles at temperature 1 in a deterministic tile assembly system satisfying a natural condition known as \emph{pumpability}, then $X$ is a finite union of semi-doubly periodic sets.…
The optical spectra of fractal multilayer dielectric structures have been shown to possess spectral scalability, which has been found to be directly related to the structure's spatial (geometrical) self-similarity. Phase and amplitude…
We show that spontaneous breaking of discrete or continuous symmetries does not necessarily imply either symmetry restoration or the thermal production of defects at high temperature (at least up to $T \sim M_{Planck}$). This may imply that…
The origin of non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Recent results indicate a connection between non-extensive statistics and thermofractals. After reviewing this connection, we…
We show that chiral symmetry can be broken spontaneously in one-component systems with isotropic interactions, i.e. many-particle systems having maximal a priori symmetry. This is achieved by designing isotropic potentials that lead to…
We discuss the phenomenon of spontaneous self-compactification in a model colloidal system, proposed in a recent work on DNA-mediated self-assembly. We focus on the effect of thermal fluctuations on the stability of membrane-like…
Polypeptides can self-assemble into hierarchically organized fibrils consisting of a stack of individually folded polypeptides driven together by hydrophobic interaction. Using a coarse grained model, we systematically studied this…
Automorphism groups of locally finite trees provide a large class of examples of simple totally disconnected locally compact groups. It is desirable to understand the connections between the global and local structure of such a group.…
We explore the use of templated self-assembly to facilitate the formation of complex target structures made from patchy particles. First, we consider the templating of high-symmetry shell structures around a spherical core particle. We find…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
We consider the numerical evaluation of a class of double integrals with respect to a pair of self-similar measures over a self-similar fractal set (the attractor of an iterated function system), with a weakly singular integrand of…
It is demonstrated that it is possible to find a field theory containing massless scalar particles which has infrared structure closely resembling that of quantum electrodynamics and perturbative quantum gravity but exhibiting no gauge…
We propose and investigate a simple model which describes the kinetics of aggregation of Brownian particles with stochastic self-replication. An exact solution and the scaling theory are presented alongside numerical simulation which fully…
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…
The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a…
The pinwheel triangle of Conway and Radin is a standard example for tilings with self-similarity and statistical circular symmetry. Many modifications were constructed, all based on partitions of triangles or rectangles. The fractal example…
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…
The well-studied Two-Handed Tile Assembly Model (2HAM) is a model of tile assembly in which pairs of large assemblies can bind, or self-assemble, together. In order to bind, two assemblies must have matching glues that can simultaneously…
The possibility to align and organize faceted particles in the bulk offers intriguing possibilities for the design and discovery of materials and architectures exhibiting novel functional properties. The growth of ice crystals can be used…
The stable fragmentation with index of self-similarity $\alpha \in [-1/2,0)$ is derived by looking at the masses of the subtrees formed by discarding the parts of a $(1 + \alpha)^{-1}$--stable continuum random tree below height $t$, for $t…