Related papers: Intersections of moving fractal sets
Two elements $g$ and $h$ of a permutation group $G$ acting on a set $V$ are said to be intersecting if $g(v) = h(v)$ for some $v \in V$. More generally, a subset ${\cal F}$ of $G$ is an intersecting set if every pair of elements of ${\cal…
The existence and uniqueness of fixed points of both the cyclic self-mapping and its associate composite self-mappings on each of the subsets are investigated if the subsets in the cyclic disposal are nonempty, bounded and of nonempty…
The onset of frictional motion at the interface between two distinct bodies in contact is characterized by the propagation of dynamic rupture fronts. We combine friction experiments and numerical simulations to study the properties of these…
This article presents the construction of a non-affine hypersurface on an $n$-simplex in $\mathbb{R}^n$. Additionally, fractal dimension of the graph of a non-affine multivariate real-valued fractal function is estimated under certain…
Diffusion of electrons in two-dimensional disordered systems with spin-orbit interactions is investigated numerically. Asymptotic behaviors of the second moment of the wave packet and of the temporal auto-correlation function are examined.…
We extend the study of the inertial effects on the dynamics of active agents to the case where self-alignment is present. In contrast with the most common models of active particles, we find that self-alignment, which couples the rotational…
Interaction between extended defects and impurities lies at the heart of many physical phenomena in materials science. Here we revisit the ubiquitous problem of the driven motion of an extended defect in a field of mobile impurities, which…
We study geometric rigidity of a class of fractals, which is slightly larger than the collection of self-conformal sets. Namely, using a new method, we shall prove that a set of this class is contained in a smooth submanifold or is totally…
This paper explores the relationship between closed curves on surfaces and their intersections. Like Dehn-Thurston coordinates for simple curves, we explore how to determine closed curves using the number of times they intersect other…
We analyse the intersection of positively and negatively sectional-hyperbolic sets for flows on compact manifolds. First we prove that such an intersection is hyperbolic if the intersecting sets are both transitive (this is false without…
Various features of the mass yields in heavy ion collisions are studied. The mass yields are discussed in terms of iterative one dimensional discrete maps. These maps are shown to produce orbits for a monomer or for a nucleus which generate…
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with…
A set partition is $c$-uniform if every block has size $c$. Two families of $c$-uniform partitions of a finite set are said to be cross $t$-intersecting if two partitions from different families share at least $t$ blocks. In this paper, we…
We investigate the influence of fractal structure on material properties. We calculate the statistical correlation functions of fractal media defined by level-cut Gaussian random fields. This allows the modeling of both surface fractal and…
It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system which is called fractal interpolation function. We generalize the notion of fractal…
Fractional Brownian motion is a self-affine, non-Markovian and translationally invariant generalization of Brownian motion, depending on the Hurst exponent $H$. Here we investigate fractional Brownian motion where both the starting and the…
The roughness of fracture surfaces has been shown to exhibit self-affne scale invariance for a wide variety of materials and loading conditions. The range of scales over which this regime extends remains a matter of debate, together with…
A recent purely theoretical prediction stated that in frictional granular packings, mechanical balance and material isotropy constrain the stress auto-correlation matrix to be fully determined by two spatially isotropic functions: the…
We show that recent observations of fractal dimensions in the $\mu$-space of $N$-body Hamiltonian systems with long-range interactions are due to finite $N$ and finite resolution effects. We provide strong numerical evidence that, in the…
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative…