Related papers: Fractal dimension of star clusters
The interstellar medium seems to have an underlying fractal structure which can be characterized through its fractal dimension. However, interstellar clouds are observed as projected two-dimensional images, and the projection of a…
Fractal nests are sets defined as unions of unit $n$-spheres scaled by a sequence of $k^{-\alpha}$ for some $\alpha>0$. In this article we generalise the concept to subsets of such spheres and find the formulas for their box counting…
Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale…
Massive star clusters are often used as tracers of galaxy formation and assembly. In order to do so, we must understand their properties at formation, and how those properties change with time, galactic environment, and galaxy assembly…
The local structure of a fractal set is described by its dimension $D$, which is the exponent of a power-law relating the mass ${\cal N}$ in a ball to its radius $\epsilon$: ${\cal N}\sim \epsilon^D$. It is desirable to characterise the…
Fractal structures emerge from statistical and hierarchical processes in urban development or network evolution. In a class of efficient and robust geographical networks, we derive the size distribution of layered areas, and estimate the…
The extent to which the projected distribution of stars in a cluster is due to a large-scale radial gradient, and the extent to which it is due to fractal sub-structure, can be quantified -- statistically -- using the measure ${\cal Q} =…
Fractal dimension is widely adopted in spatial databases and data mining, among others as a measure of dataset skewness. State-of-the-art algorithms for estimating the fractal dimension exhibit linear runtime complexity whether based on…
Star clusters stand at the intersection of much of modern astrophysics: the interstellar medium, gravitational dynamics, stellar evolution, and cosmology. Here we review observations and theoretical models for the formation, evolution, and…
The evolution of star clusters is studied using N-body simulations in which the evolution of single stars and binaries are taken self-consistently into account. Initial conditions are chosen to represent relatively young Galactic open…
Background: Neutron stars are astronomical systems with nucleons submitted to extreme conditions. Due to the long range coulomb repulsion between protons, the system has structural inhomogeneities. These structural inhomogeneities arise…
Fractal scaling--a power-law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box--is studied. We introduce a new box-covering algorithm that is a modified version of the original…
Most gas in giant molecular clouds is relatively low-density and forms star inefficiently, converting only a small fraction of its mass to stars per dynamical time. However, star formation models generally predict the existence of a…
Open and globular star clusters have served as benchmarks for the study of stellar evolution due to their supposed nature as simple stellar populations of the same age and metallicity. After a brief review of some of the pioneering work…
In this work, we develop a statistical analysis of the large-scale clustering of matter in the Universe from the fractal point of view using galaxies from the Ninth Sloan Digital Sky Survey (SDSS) Data Release (DR9). From the total set of…
The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored…
The incipient infinite cluster appearing at the bond percolation threshold can be decomposed into singly-connected ``links'' and multiply-connected ``blobs.'' Here we decompose blobs into objects known in graph theory as 3-blocks. A 3-block…
We perform N-body simulations of a cluster that forms in a dwarf galaxy and is then accreted by the Milky Way to investigate how a cluster's structure is affected by a galaxy merger. We find that the cluster's half mass radius will respond…
Considering the GAIA data for {$\approx 10^6$} stars around the {barycenter,} we estimate the fractal dimension for different regions in the Milky Way. Then we use those fractal dimensions to calculate the gravitational potential…
Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several…