Related papers: Determining the Fractal Dimension of the Interstel…
We use a spatially resolved cavity ring-down technique to show that the 2D eigenmode of an unstable optical cavity has a fractal pattern, i.e. it looks the same at different length scales. In agreement with theory, we find that this pattern…
Fractal surfaces are ubiquitous in nature as well as in the sciences. The examples range from the cloud boundaries to the corroded surfaces. Fractal dimension gives a measure of the irregularity in the object under study. We present a…
In the interstellar medium of the Milky Way, certain elements -- e.g., Mg, Si, Al, Ca, Ti, Fe -- reside predominantly in interstellar dust grains. These grains absorb, scatter, and emit electromagnetic radiation, heat the interstellar…
Observations of H3+ in the Galactic diffuse interstellar medium (ISM) have led to various surprising results, including the conclusion that the cosmic-ray ionization rate (zeta_2) is about 1 order of magnitude larger than previously…
Using Monte Carlo simulations we study the distributions of the 3-block mass $N_3$ in 4d, 5d, and 6d percolation systems. Because the probability of creating large 3-blocks in these dimensions is very small, we use a ``go with the winners''…
Perfect fractals are mathematical objects that, because they are generated by recursive processes, have self-similarity and infinite complexity. In particular, they also have a fractional dimension. Although several proposals for the study…
I present an overview of the hierarchy of structures existing in the interstellar medium (ISM) and the possible mechanisms that cause the fragmentation of one level into the next, with the formation of stars as its last step. Within this…
We map the distribution and properties of the Milky Way's interstellar medium as traced by diffuse interstellar bands (DIBs) detected in near-infrared stellar spectra from the SDSS-III/APOGEE survey. Focusing exclusively on the strongest…
This work tests if the large-scale galaxy distribution can be characterized as a fractal system. The $\Lambda$CDM cosmology with $H_0=(70\pm 5)$ km/s/Mpc is adopted to study the UltraVISTA DR1, COSMOS2015 and SPLASH surveys, alongside the…
A fractal surface is a set which is a graph of a bivariate continuous function. In the construction of fractal surfaces using IFS, vertical scaling factors in IFS are important one which characterizes a fractal feature of surfaces…
The possibility to constrain fractal space dimensionality from Astrophysics and other areas is briefly reviewed. Assuming such dimensionality to be $3 + \epsilon$, a limit to $\epsilon$ can be inferred from COBE satellite data. The…
This report focuses on the dependencies for the center and radius of the confidence interval that arise when estimating the mass fractal dimensions of isotropic sampling clusters in the site percolation model.
We analyze the physical parameters of interstellar filaments that we describe by an idealized model of isothermal self-gravitating infinite cylinder in pressure equilibrium with the ambient medium. Their gravitational state is characterized…
Galaxy structures are certainly fractal up to a certain crossover scale \lambda_0. A clear determination of such a scale is still missing. Usually, the conceptual and practical implications of this property are neglected and the structures…
Spatial patterns and processes of cities can be described with various entropy functions. However, spatial entropy always depends on the scale of measurement, and it is difficult to find a characteristic value for it. In contrast, fractal…
The thermal properties of star-forming clouds have an important influence on how they fragment into stars, and it is suggested in this paper that the low-mass stellar IMF, which appears to be almost universal, is determined largely by the…
A \emph{fractal} is an object exhibiting complexity at arbitrarily small scales. In order to study and characterise fractals, one is often interested in quantifying how they fill up space on small scales. This gives rise to various notions…
This paper studies the effect of the distance choice in radial (non-average) statistical tools used for fractal characterization of galaxy distribution. After reviewing the basics of measuring distances of cosmological sources, various…
Despite the observational evidence that the Universe appears hierarchically structured up to a distance of at least 30 Mpc/h (and possibly up to 100 Mpc/h), the fractal paradigm has not yet been recognized by the majority of cosmologists…
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…