Related papers: Apparent fractal dimensions in the HMF model
The aim of this paper is to find an upper bound for the box-counting dimension of uniform attractors for non-autonomous dynamical systems. Contrary to the results in literature, we do not ask the symbol space to have finite box-counting…
The Hausdorff fractal dimension has been a fast-to-calculate method to estimate complexity of fractal shapes. In this work, a modified version of this fractal dimension is presented in order to make it more robust when applied in estimating…
We prove that the fractal dimension of a metric space equipped with an Ahlfors regular measure can be recovered from the persistent homology of random samples. Our main result is that if $x_1,\ldots, x_n$ are i.i.d. samples from a…
We develop the hypothesis that the dynamics of a given system may lead to the activity being constricted to a subset of space, characterized by a fractal dimension smaller than the space dimension. We also address how the response function…
The Hamiltonian of mean force (HMF) provides the standard starting point for strong-coupling thermodynamics, yet explicit operator forms are known only in restricted settings. We present a quenched density framework that uses 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…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
Two-point correlation function of galaxy distribution shows that the structure in the present Universe is scale-free up to a certain scale (at least several tens Mpc), which suggests that a fractal structure may exist. If small primordial…
We study the Hausdorff and box-counting dimensions of cookie-cutter-like sets formed by sequential dynamics of a finite number of expanding maps. Under some natural conditions, these dimensions turn out to be the minimum and maximum of the…
Patterns formed by the flow of an inhomogeneous fluid (suspension) over a smooth inclined surface were studied. It was observed that for inclination angle larger than a threshold, global fractal patterns are formed. The fractal dimensions…
The Hamiltonian Mean Field (HMF) model describes particles on a ring interacting via a cosine interaction, or equivalently, rotors coupled by infinite-range XY interactions. Conceived as a generic statistical mechanical model for long-range…
This study develops a comprehensive theoretical and computational framework for Random Nonlinear Iterated Function Systems (RNIFS), a generalization of classical IFS models that incorporates both nonlinearity and stochasticity. We establish…
The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…
We consider subsets of the (symbolic) sequence space that are invariant under the action of the semigroup of multiplicative integers. A representative example is the collection of all 0-1 sequences $(x_k)$ such that $x_k x_{2k}=0$ for all…
Hausdorff dimensions of level sets of generic continuous functions defined on fractals can give information about the "thickness/narrow cross-sections'' of a "network" corresponding to a fractal set, $F$. This lead to the definition of the…
We introduce a duality for Affine Iterated Function Systems (AIFS) which is naturally motivated by group duality in the context of traditional harmonic analysis. Our affine systems yield fractals defined by iteration of contractive affine…
The $\lambda \phi^4$ model in a finite volume is studied within a non-gaussian Hartree-Fock approximation (tdHF) both at equilibrium and out of equilibrium, with particular attention to the structure of the ground state and of certain…
The image fractal analysis is actively used in all science branches. In particular in materials science the fractal analysis is applied to study microstructure of deformed metals because its structure can be interpreted as the fractal…
The relation between critical exponents, characterizing a continuous phase transition, and the fractal structure of physical lines, proliferating at the critical point, is established by considering the two-dimensional O($N$) spin model for…
Motivated by applications in number theory, analysis, and fractal geometry, we consider regularity properties and dimensions of graphs associated with Fourier series of the form $F(t)=\sum_{n=1}^\infty f(n)e^{2\pi i nt}/n$, for a large…