Related papers: Fractal dimension in star formation regions
Three dimensional (3D) distribution of the volume-density molecular fraction, defined by fmol_rho=rho_H2/(rho_HI + rho_H2), is studied in the Milky Way Galaxy. The molecular front appears at galacto-centric distance of R \sim 8 kpc, where…
Many young star clusters appear to be fractal, i.e. they appear to be concentrated in a nested hierarchy of clusters within clusters. We present a new algorithm for statistically analysing the distribution of stars to quantify the level of…
About two-thirds of disk galaxies host spiral arms, ranging from well-delineated grand-design spirals to fragmented flocculent spiral galaxies. We introduce fractal dimension $D_B$ as a non-parametric measure to distinguish between…
CONTEXT: Cosmic voids are observed in the distribution of galaxies and, to some extent, in the dark matter distribution. If these distributions have fractal geometry, it must be reflected in the geometry of voids; in particular, we expect…
In this article, we investigate the fractal dimension of the graph of the mixed Riemann-Liouville fractional integral for various choice of continuous functions on a rectangular region. We estimate bounds for the box dimension and the…
\emph{Fractal percolation} or \emph{Mandelbrot percolation} is one of the most well studied families of random fractals. In this paper we study some of the geometric measure theoretical properties (dimension of projections and structure of…
To investigate the process of star formation triggered by the expansion of an HII region, we present a multi-wavelength analysis of the Galactic HII region RCW 120 and its surroundings. The collect and collapse model predicts that the layer…
This paper discusses if large scale galaxy distribution samples containing almost one million objects can be characterized as fractal systems. The analysis performed by Teles et al. (2021; arXiv:2012.07164) on the UltraVISTA DR1 survey is…
We present results of a method for an automatic search for HI shells in 3D data cubes and apply it to the Leiden-Dwingeloo HI survey of the northern Milky Way. In the 2nd Galactic quadrant, where identifications of structures are not…
Supersonic turbulence is a key player in controlling the structure and star formation potential of molecular clouds (MCs). The three-dimensional (3D) turbulent Mach number, $\mathcal{M}$, allows us to predict the rate of star formation.…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
We study the three-dimensional structure of the Milky Way using 65,981 Mira variable stars discovered by the Optical Gravitational Lensing Experiment (OGLE) survey. The spatial distribution of the Mira stars is analyzed with a model…
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…
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension $d$ ($1 \leq d \leq 3$) are developed as heuristic interpolations from the knowledge of…
We study the porosity properties of fractal percolation sets $E\subset\mathbb{R}^d$. Among other things, for all $0<\varepsilon<\tfrac12$, we obtain dimension bounds for the set of exceptional points where the upper porosity of $E$ is less…
We present measurements of the fractal dimension of a turbulent asymptotically anti-deSitter black brane reconstructed from simulated boundary fluid data at the perfect fluid order using the fluid-gravity duality. We argue that the boundary…
In this paper, we discuss the Higuchi algorithm which serves as a widely used estimator for the box-counting dimension of the graph of a bounded function $f : [0,1] \to \R$. We formulate the method in a mathematically precise way and show…
In this paper we have defined two functions that have been used to construct different fractals having fractal dimensions between 1 and 2. More precisely, we can say that one of our defined functions produce the fractals whose fractal…
Fractal dimension constitutes the main tool to test for fractal patterns in Euclidean contexts. For this purpose, it is always used the box dimension, since it is easy to calculate, though the Hausdorff dimension, which is the oldest and…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…