Related papers: Fractal dimension in star formation regions
Accurately reproducing the thin cold gas discs observed in nearby spiral galaxies has been a long standing issue in cosmological simulations. Here, we present measurements of the radially resolved HI scale height in 22 non-interacting Milky…
Observations of HI published in 1957 by Westerhout and Schmidt were presented as showing a global face-on view of spiral structure in the Milky Way. Since then many studies have attempted to improve on the early map, perhaps presupposing…
We developed a new selection method of halo stars in the phase-space distribution defined by the three integrals of motion in an axisymmetric Galactic potential, ($E$, $L_z$, $I_3$), where $I_3$ is the third integral of motion. The method…
A representation of frequency of strings of length K in complete genomes of many organisms in a square has led to seemingly self-similar patterns when K increases. These patterns are caused by under-represented strings with a certain…
We calculated spatial correlation functions of galaxies, $\xi(r)$, structure functions, $g(r)=1 +\xi(r)$, gradient functions, $\gamma(r)= d \log g(r)/ d \log r$, and fractal dimension functions, $D(r)= 3+\gamma(r)$, using dark matter…
In order to test the reliability of determinations of the shapes of galaxies' dark matter halos, we have made such measurements for the Milky Way by two independent methods, which make use of the stellar kinematics in the solar…
We examine the proposal that a model of the large-scale matter distribution consisting of randomly placed haloes with power-law profile, as opposed to a fractal model, can account for the observed power-law galaxy-galaxy correlations. We…
The Schmidt law (SF law) in the Milky Way was investigated using 3D distribution maps of HII regions, HI and molecular (\Htwo) gases with spatial resolutions of $\sim 1$ kpc in the Galactic plane and a few tens of pc in the vertical…
\begin{abstract} $\pi$, the ratio between a circumference and is radius, is an irrational transcendental number. Fractal analysis is used here to show that $\pi$\textquoteright{s} digit sequence corresponds to a uniformly distributed random…
Aims: We systematically explore a plausible subset of the parameter space involving effective temperatures and metallicities of the ionizing stellar sources, the effects of the hardening of their radiation by surrounding leaky HII regions…
In protoplanetary discs and planetary atmospheres, dust grains coagulate to form fractal dust aggregates. The geometric cross-section of these aggregates is a crucial parameter characterizing aerodynamical friction, collision rates, and…
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…
It is shown that calculus can apply on a fractal structure with the condition that the infinitesimal limit of change of the variable is larger than the lower cut-off of the fractal structure, and an assumption called local decomposability.…
We have mapped the number density and mean vertical velocity of the Milky Way's stellar disk out to roughly two kiloparsecs from the Sun using Gaia Data Release 3 (DR3) and complementary photo-astrometric distance information from…
Many 0/1 datasets have a very large number of variables; on the other hand, they are sparse and the dependency structure of the variables is simpler than the number of variables would suggest. Defining the effective dimensionality of such a…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
A well studied family of random fractals called fractal percolation is discussed. We focus on the projections of fractal percolation on the plane. Our goal is to present stronger versions of the classical Marstrand theorem, valid for almost…
We investigate dimension-theoretic properties of concentric topological spheres, which are fractal sets emerging both in pure and applied mathematics. We calculate the box dimension and Assouad spectrum of such collections, and use them to…
The Palomar Integral Field Spectrograph was used to probe a variety of environments in nine nearby galaxies that span a range of morphological types, luminosities, metallicities, and infrared-to-blue ratios. For the first time,…
We derived the three-dimensional distribution of HI gas in the Milky Way Galaxy using the latest HI survey data cubes and rotation curves. The distance of the HI gas was determined by the kinematic distance using a rotation curve. We solved…