Related papers: The impressive complexity in the Nautilus pompiliu…
Cohesive particles form agglomerates that are usually very porous. Their geometry, particularly their fractal dimension, depends on the agglomeration process (diffusion-limited or ballistic growth by adding single particles or…
The structural evolution of a nano-powder by repeated dispersion and settling can lead to characteristic fractal substructures. This is shown by numerical simulations of a two-dimensional model agglomerate of adhesive rigid particles. The…
Much is known in the analysis of a finitely ramified self-similar fractal when the fractal has a harmonic structure: a Dirichlet form which respects the self-similarity of a fractal. What is still an open question is when such structure…
Abstract Self-similar, fractal nature of turbulence is discussed in the context of two dimensional turbulence, by considering the fractal structure of the wave-number domain using spirals. In loose analogy with phyllotaxis in plants, each…
We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…
We investigate critical properties of a spatial evolutionary game based on the Prisoner's Dilemma. Simulations demonstrate a jump in the component densities accompanied by drastic changes in average sizes of the component clusters. We argue…
The self-assembly of polyhedral shells, each constructed from 60 trapezoidal particles, is simulated using molecular dynamics. The spatial organization of the component particles in this shell is similar to the capsomer proteins forming the…
We investigate fractal aspects of elliptical polynomial spirals; that is, planar spirals with differing polynomial rates of decay in the two axis directions. We give a full dimensional analysis of these spirals, computing explicitly their…
Results from molecular dynamics simulations of simple, structured particles capable of self-assembling into polyhedral shells are described. The analysis focuses on the growth histories of individual shells in the presence of an explicit…
Ammonoids are a group of extinct mollusks belonging to the same class of the living genus Nautilus (Cephalopoda). In both Nautili and ammonoids, the (usually planospiral) shell is divided into chambers separated by septa that during the…
We investigate dimension-theoretic properties of concentric topological spheres, which are fractal sets emerging both in pure and applied mathematics. We calculate the box dimension and Assouad spectrum of such collections, and use them to…
A theoretical model for fractal growth of DLA-clusters in two- and three-dimensional Euclidean space is proposed. This model allows to study some statistical properties of growing clusters in two different situations: in the static case…
The fractal properties of four-dimensional Euclidean simplicial manifold generated by the dynamical triangulation are analyzed on the geodesic distance D between two vertices instead of the usual scale between two simplices. In order to…
We study, both with numerical simulations and theoretical methods, a cellular automata model for continuum equations describing growth processes in the presence of an external flux of particles. As a result of local instabilities we find a…
Analysis of experimental kinetic dependences and results of the computer modeling of pairwise interactions in the heterogeneous system have shown that a character of its fractal property variation in the evolution process would be different…
In this work, we examine the relationship between geometry and spectrum of regions with fractal boundary. The relationship is well-understood for fractal harps in one dimension, but largely open for fractal drums in larger dimensions. To…
We present a detailed systematical theoretical analysis of the post-growth processes occurring in nanofractals grown on surface. For this study we developed a method which accounts for the internal dynamics of particles in a fractal. We…
Bimodal cellular poly(methyl methacrylate) with micron and nano sized (300 to 500 nm) cells with up to 5 weight percent of sepiolite nanoparticles and porosity from 50 weight percent to 75 weight percent are produced by solid state foaming.…
We model shell formation of core-shell noble metal nanoparticles. A recently developed kinetic Monte Carlo approach is utilized to reproduce growth morphologies realized in recent experiments on core-shell nanoparticle synthesis, which…
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…