Related papers: On the Evolution During Growth of Regular Boundari…
The material structure of bodies undergoing growth is considered. In the geometric framework of a general differential manifold modeling the physical space and a fiber bundle modeling spacetime, body points may be defined for any extensive…
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…
We prove the existence of fractal solutions to a class of linear ordinary differential equations.This reveals the possibility of chaos in the very short time limit of the evolution even of a linear one dimensional dynamical system.
The evolution and spatial structure of displacement fronts in fractures with self-affine rough walls are studied by numerical simulations. The fractures are open and the two faces are identical but shifted along their mean plane, either…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…
We consider the volume preserving geometric evolution of the boundary of a set under fractional mean curvature. We show that smooth convex solutions maintain their fractional curvatures bounded for all times, and the long time asymptotics…
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…
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…
We study the kinetics of random sequential adsorption of a mixture of particles with continuous distribution of sizes for different deposition rules. It appears in the long time limit the resulting system can be described using the fractal…
The free volume comprised between rough surfaces in contact governs the fluid/gas transport properties across networks of cracks and the leakage/percolation phenomena in seals. In this study, a fundamental insight into the evolution of the…
Fractals are defined as geometric shapes that exhibit symmetry of scale. This simply implies that fractal is a shape that it would still look the same even if somebody could zoom in on one of its parts an infinite number of times. This…
Granular flows down inclined channels with smooth boundaries are common in nature and in the industry. Nevertheless, the common setup of flat boundaries has comparatively been much less investigated than the bumpy boundaries one, which is…
Urbanization is a phenomenon of concern for planning and public health: projections are difficult because of policy changes and natural events, and indicators are multiple. There are previous studies of development that used fractals, but…
Fractals emerge everywhere in nature, exhibiting intricate geometric complexities through the self-organizing patterns that span across multiple scales. Here, we investigate beyond steady-states the interplay between this geometry and the…
We consider the evolution by crystalline curvature of a planar set in a stratified medium, modeled by a periodic forcing term. We characterize the limit evolution law as the period of the oscillations tends to zero. Even if the model is…
We simulate the gravitational dynamics of the conifold geometries (resolved and deformed) involved in the description of certain compact spacetimes. As the cycles of the conifold collapse towards a singular geometry we find that a horizon…
In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish evolutions…
In this paper, we extend the classical de Rham decomposition theorem to the case of Riemannian manifolds with boundary by using the trick of development of curves.
Stochastic growth processes give rise to diverse intricate structures everywhere and across all scales in nature. Despite the seemingly unrelated complex phenomena at their origin, the Laplacian growth theory has succeeded in unifying their…
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…