Related papers: Deterministic fractals: extracting additional info…
Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities…
This paper introduces the concept of Fractal Frenet equations, a set of differential equations used to describe the behavior of vectors along fractal curves. The study explores the analogue of arc length for fractal curves, providing a…
Experiments in which thick clay plates and glass rods are fractured have revealed different behavior of fragment mass distribution function in the small and large fragment regions. In this paper we explain this behavior using non-extensive…
The fractal dimensions of polymer chains and high-temperature graphs in the Ising model both in three dimension are determined using the conformal bootstrap applied for the continuation of the $O(N)$ models from $N=1$ (Ising model) to $N=0$…
Fractal dimension is an effective scaling exponent of characterizing scale-free phenomena such as cities. Urban growth can be described with time series of fractal dimension of urban form. However, how to explain the factors behind fractal…
We report a clear evidence of atomic fractals in the nonlinear motion of a two-level atom in a standing-wave microcavity. Fractal-like structures, typical for chaotic scattering, are numerically found in the dependencies of outgoing…
It is shown that piecewise deterministic dissipative quantum dynamics in a vector space with indefinite metric can lead to well defined, positive probabilities. The case of quantum jumps on the Poincar'e disk is studied in details,…
The available experimental information is consistent with the Weinberg predictions for the threshold parameters of pi-pi-scattering. The data, however, only test those relations that are insensitive to the quark masses m_u and m_d. Recent…
The emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In this work we carry out a detailed renormalization group study of the spectral dimension $d_s$ and walk…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
We argued that deep inelastic scattering (DIS) at small values of Q squared is an essentially nonperturbative process and can be described, partially at least, by the vector meson dominance (VMD) model. We showed by the straightforward…
For small volume of the quark-gluon plasma formed in heavy ion collisions, the observable near criticality must obey finite-size scaling. According to the finite-size scaling, there exists a fixed point at the critical temperature, where…
Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation…
We consider the time dependent dispersion properties of overdamped tracer particles diffusing in a one dimensional periodic potential under the influence of an additional constant tilting force $F$. The system is studied in the region where…
We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically…
A numerical realization of an elastic beam lattice is used to obtain scaling exponents relevant to the extent of damage within the controlled, catastrophic and total regimes of mode-I brittle fracture. The relative fraction of damage at the…
We investigate the evolution of the density-density correlations in the isoscalar critical condensate formed at the QCD critical point. The initial equilibrium state of the system is characterized by a fractal measure determining the…
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight…
We present a review of the history and the present state of the fractal approach to the large-scale distribution of galaxies. Angular correlation function was used as a general instrument for the structure analysis. It was realized later…