Related papers: Scaled tree fractals do not strictly self-assemble
In self-assembling systems, geometric frustration leads to complex states characterized by internal gradients of shape misfit. Frustrated assemblies have drawn recent interest due to the unique possibility that their thermodynamics can…
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…
During the last decade, self-affine geometrical properties of many growing aggregates, originated in a wide variety of processes, have been well characterized. However, little progress has been achieved in the search of a unified…
Colloidal particles can self-assemble into various ordered structures in fluid flows that have potential applications in biomedicine, materials synthesis and encryption. These dynamic processes are also of fundamental interest for probing…
Clouds in observations are fractals: they show self-similarity across scales ranging from one to 1000 km. This includes individual storms and large-scale cloud structures typical of organised convection. It is not known whether global…
We show how clustering as a general hierarchical dynamical process proceeds via a sequence of inverse cascades to produce self-similar scaling, as an intermediate asymptotic, which then truncates at the largest spatial scales. We show how…
When strained beyond the linear regime, soft colloidal glasses yield to steady-state plastic flow in a way that is similar to the deformation of conventional amorphous solids. Due to the much larger size of the colloidal particles with…
Is Winfree's abstract Tile Assembly Model (aTAM) "powerful?" Well, if certain tiles are required to "cooperate" in order to be able to bind to a growing tile assembly (a.k.a., temperature 2 self-assembly), then Turing universal computation…
Conserved quantities are obtained and analyzed in the new models with global scale invariance recently proposed. Such models allow for non tivial scalar field potentials and masses for particles, so that the scale symmetry must be broken…
In this article a collection of random self-similar fractal dendrites is constructed, and their Hausdorff dimension is calculated. Previous results determining this quantity for random self-similar structures have relied on geometrical…
In this paper we construct a self-similar fractal configured as an infinitely branched tree and equip it with a regular self-similar Dirichlet form. We show anomalous behaviour of the mean exit time with respect to typical metric balls.…
An important problem in the analysis of experimental data showing fractal properties, is that such samples are composed by a set of points limited by an upper and a lower cut off. We study how finite size effect due to the discreteness of…
We introduce an analytically solvable model for a fragmented object that, despite of a low degree of randomness and of the extreme simplicity of the breaking process, displays non self-averaging effects in its thermodynamic limit.
The self-similar structure of the attracting subshift of a primitive substitution is carried over to the limit set of the repelling tree in the boundary of Outer Space of the corresponding irreducible outer automorphism of a free group.…
We study the percolation phase transition in hierarchical scale-free nets. Depending on the method of construction, the nets can be fractal or small-world (the diameter grows either algebraically or logarithmically with the net size),…
A simple scaling theory for the sintering of fractal aerogels is presented. The densification at small scales is described by an increase of the lower cut-off length $a$ accompanied by a decrease of the upper cut-off length $\xi$, in order…
In contrast to the conventional wisdom that scale-free networks are prone to epidemic propagation, in the paper we present that disease spreading is inhibited in fractal scale-free networks. We first propose a novel network model and show…
We generalize the compatible tower condition given by Strichartz to the almost-Parseval-frame tower and show that non-trivial examples of almost-Parseval-frame tower exist. By doing so, we demonstrate the first singular fractal measure…
We present a generic model to describe the fractal self-assembly of proteins in terms of electrostatic and hydrophobic interactions. The predictions of the model were correlated with the simulated fractals obtained using patchy…
We systematically investigate the self-assembly of anisotropic cone-shaped particles decorated by ring-like attractive patches. We demonstrate that the self-assembled clusters, which arise due to the conical particle's anisotropic shape…