ON THE DYNAMICAL EVOLUTION OF THE FRACTAL STRUCTURE OF INTERSTELLAR MEDIUM

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 908-916 ◽  
Author(s):  
Z.Y. YUE ◽  
B. ZHANG ◽  
G. WINNEWISSER ◽  
J. STUTZKI
Keyword(s):  
Fractal Dimension ◽  
Interstellar Medium ◽  
Density Distribution ◽  
Fractal Structure ◽  
Initial Conditions ◽  
Initial Density ◽  
Dynamical Evolution ◽  
Fractal Dimensions ◽  
Compressible Turbulence ◽  
Initial States

Two-dimensional compressible turbulence in a self-gravitating, magnetic interstellar medium is calculated as an initial value problem. It is shown that even if the initial density distribution is homogeneous and the initial velocity distribution contains only a few Fourier components, the nonlinear interaction among the Fourier components will generate more and more Fourier components and lead to a turbulent and fractal structure in the interstellar medium. The calculations are carried out for three different initial states. In order to see the time evolution, detailed density distributions and fractal dimensions of the density contours are calculated at three moments of time for each of the initial states. The results show that the fractal dimension remains almost the same (~1.4–1.5), although the detailed density distribution has changed considerably. The insensibility of the fractal dimension of density contours to both the initial conditions and the evolution time is in good agreement with observations of molecular clouds in the interstellar medium.

scholarly journals The linkage between box-counting and geomorphic fractal dimensions in the fractal structure of river networks: the junction angle

2020 ◽  
Vol 51 (6) ◽  
pp. 1397-1408
Author(s):  
Xianmeng Meng ◽  
Pengju Zhang ◽  
Jing Li ◽  
Chuanming Ma ◽  
Dengfeng Liu
Keyword(s):  
Fractal Dimension ◽  
Fractal Structure ◽  
Fractal Dimensions ◽  
River Networks ◽  
Stream Length ◽  
Box Counting ◽  
Linear Relationships ◽  
Box Counting Dimension ◽  
Junction Angle

Abstract In the past, a great deal of research has been conducted to determine the fractal properties of river networks, and there are many kinds of methods calculating their fractal dimensions. In this paper, we compare two most common methods: one is geomorphic fractal dimension obtained from the bifurcation ratio and the stream length ratio, and the other is box-counting method. Firstly, synthetic fractal trees are used to explain the role of the junction angle on the relation between two kinds of fractal dimensions. The obtained relationship curves indicate that box-counting dimension is decreasing with the increase of the junction angle when geomorphic fractal dimension keeps constant. This relationship presents continuous and smooth convex curves with junction angle from 60° to 120° and concave curves from 30° to 45°. Then 70 river networks in China are investigated in terms of their two kinds of fractal dimensions. The results confirm the fractal structure of river networks. Geomorphic fractal dimensions of river networks are larger than box-counting dimensions and there is no obvious relationship between these two kinds of fractal dimensions. Relatively good non-linear relationships between geomorphic fractal dimensions and box-counting dimensions are obtained by considering the role of the junction angle.

A New Method of Characterization on Microstructure of Casting Alloy

2011 ◽  
Vol 211-212 ◽  
pp. 122-126
Author(s):  
Zheng Liu ◽  
Xiao Mei Liu
Keyword(s):  
Fractal Dimension ◽  
Fractal Structure ◽  
A356 Alloy ◽  
Fractal Dimensions ◽  
Primary Phase ◽  
New Method ◽  
Casting Alloy ◽  
Microstructural Characteristics ◽  
Low Superheat

Microstructural characteristics of A356 alloy prepared by low superheat pouring were researched, and the fractal dimensions of morphology of primary phase in the alloy was calculated. The results indicated that morphology of primary phase in A356 alloy belonged to fractal structure, and the microstructural characteristics in the alloy can be characterized by fractal dimension. There were the different fractal dimensions for the morphology of primary phase prepared by the different process.

scholarly journals Dynamical evolution of fractal structures in star-forming regions

2020 ◽  
Vol 493 (4) ◽  
pp. 4925-4935
Author(s):  
Emma C Daffern-Powell ◽  
Richard J Parker
Keyword(s):  
Minimum Spanning Tree ◽  
Initial Conditions ◽  
Average Length ◽  
Dynamical Evolution ◽  
Fractal Dimensions ◽  
Fractal Structures ◽  
Nearby Star ◽  
Star Forming ◽  
Star Forming Regions ◽  
Set Up

ABSTRACT The $\mathcal {Q}$-parameter is used extensively to quantify the spatial distributions of stars and gas in star-forming regions as well as older clusters and associations. It quantifies the amount of structure using the ratio of the average length of the minimum spanning tree, $\bar{m}$, to the average length within the complete graph, $\bar{s}$. The interpretation of the $\mathcal {Q}$-parameter often relies on comparing observed values of $\mathcal {Q}$, $\bar{m}$, and $\bar{s}$ to idealized synthetic geometries, where there is little or no match between the observed star-forming regions and the synthetic regions. We measure $\mathcal {Q}$, $\bar{m}$, and $\bar{s}$ over 10 Myr in N-body simulations, which are compared to IC 348, NGC 1333, and the ONC. For each star-forming region, we set up simulations that approximate their initial conditions for a combination of different virial ratios and fractal dimensions. We find that the dynamical evolution of idealized fractal geometries can account for the observed $\mathcal {Q}$, $\bar{m}$, and $\bar{s}$ values in nearby star-forming regions. In general, an initially fractal star-forming region will tend to evolve to become more smooth and centrally concentrated. However, we show that different initial conditions, as well as where the edge of the region is defined, can cause significant differences in the path that a star-forming region takes across the $\bar{m}{-}\bar{s}$ plot as it evolves. We caution that the observed $\mathcal {Q}$-parameter should not be directly compared to idealized geometries. Instead, it should be used to determine the degree to which a star-forming region is either spatially substructured or smooth and centrally concentrated.

scholarly journals The Evolution of Young Supernova Remnants

1983 ◽  
Vol 101 ◽  
pp. 119-124
Author(s):  
A. C. Fabian ◽  
W. Brinkmann ◽  
G. C. Stewart
Keyword(s):  
Density Distribution ◽  
Stellar Wind ◽  
Supernova Remnants ◽  
Initial Conditions ◽  
Numerical Models ◽  
Variable Mass ◽  
Initial Density ◽  
X Ray ◽  
Cassiopeia A ◽  
Initial Density Distribution

Einstein X-ray observations of the young supernova remnants Cassiopeia A (Murray et al. 1980) and Tycho (Seward, Gorenstein and Tucker 1982) indicate that the swept-up mass does not much exceed that of the observed ejecta. The initial density distribution of the ejecta and surrounding material is then important in determining the X-ray structure and evolution. Some aspects of this behaviour have been dealt with in previous numerical (e.g. Gull 1973; Itoh 1977; Jones, Smith and Straka 1981) and analytical (e.g. Chevalier 1982a,b) studies. We present here results obtained from numerical models covering a wider range of initial conditions. In particular, we consider the effect of a constant stellar wind from the progenitor star on the expansion of the remnant. We have previously suggested that variable mass loss from SN1006 may explain its warm filled interior (Fabian, Stewart and Brinkmann 1982).

Fractal Structure of Au Geochemical Field for Shuikoushan Orefield in Hunan Province, China and its Application to Mineralization

2015 ◽  
Vol 1092-1093 ◽  
pp. 1398-1401 ◽  
Author(s):  
Yan Shi Xie ◽  
Jian Wen Yin ◽  
Kai Xuan Tan ◽  
Liang Chen ◽  
Yang Hu ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Large Scale ◽  
Fractal Structure ◽  
Fractal Dimensions ◽  
Hunan Province ◽  
Small Scale ◽  
Fractal Measure ◽  
Mafic Magmatism ◽  
Covering Method ◽  
Polymetallic Ore

The fractal measure on Au geochemical field of Mawangtang and Xinmengshan in Shuikoushan Pb-Zn-Au polymetallic ore field, Hunan, China was achieved by projective covering method in this paper. The results show a bifractal relation for Au Geochemical field which includes a textural fractal dimension (D1) at small scale and a structural fractal dimension (D2) at large scale with average breakpoint 86.0m which may be look as the movement scale of ore-forming fluid. All of fractal dimensions were between 2 to 3, D1 was 2.0011 and D2 was 2.0001 at Mawangtang as well as D1 was 2.4466 and D2 was 2.0408 at Xinmengshan respectively. The fractal dimensions appear the textural fractal dimensions were larger than their structural fractal dimensions indicate that the evolution of ore-forming fluid more complex than background value of this ore field. And what’s more, the fractal values of Mawangtang were larger than Xinmengshan may result from the mineralization with the former not only control by the overthrust structure and fold the same as the latter but also had a closed relationship with the acid to mafic magmatism.

ON THE DYNAMICAL EVOLUTION OF THE FRACTAL STRUCTURE OF INTERSTELLAR MEDIUM

1994 ◽  
pp. 515-523
Author(s):  
Z. Y. YUE ◽  
B. ZHANG ◽  
G. WINNEWISSER ◽  
J. STUTZKI
Keyword(s):  
Interstellar Medium ◽  
Fractal Structure ◽  
Dynamical Evolution

scholarly journals On the grain-sized distribution of turbulent dust growth

2020 ◽  
Vol 499 (4) ◽  
pp. 6035-6043
Author(s):  
Lars Mattsson
Keyword(s):  
Interstellar Medium ◽  
Density Distribution ◽  
Rate Of Change ◽  
Compressible Turbulence ◽  
Dust Grains ◽  
Gas Density ◽  
Wide Range ◽  
The Mean ◽  
High Mach ◽  
Special Case

ABSTRACT It has recently been shown that turbulence in the interstellar medium can significantly accelerate the growth of dust grains by accretion of molecules, but the turbulent gas density distribution also plays a crucial role in shaping the grain-sized distribution (GSD). The growth velocity, i.e. the rate of change of the mean grain radius, is proportional to the local gas density if the growth species (molecules) are well mixed in the gas. As a consequence, grain growth happens at vastly different rates in different locations, since the gas density distribution of the interstellar medium (ISM) shows a considerable variance. Here, it is shown that GSD rapidly becomes a reflection of the gas density distribution, irrespective of the shape of the initial GSD. This result is obtained by modelling ISM turbulence as a Markov process, which in the special case of an Ornstein–Uhlenbeck process leads to a lognormal gas density distribution, consistent with numerical simulations of isothermal compressible turbulence. This yields an approximately lognormal GSD; the sizes of dust grains in cold ISM clouds may thus not follow the commonly adopted power-law GSD with index −3.5 but corroborate the use of a lognormal GSD for large grains, suggested by several studies. It is also concluded that the very wide range of gas densities obtained in the high Mach-number turbulence of molecular clouds must allow formation of a tail of very large grains reaching radii of several microns.

Rapid determination of fractal structure of bacterial assemblages in wastewater treatment: implications to process optimisation

1998 ◽  
Vol 38 (2) ◽  
pp. 9-15 ◽  
Author(s):  
J. Guan ◽  
T. D. Waite ◽  
R. Amal ◽  
H. Bustamante ◽  
R. Wukasch
Keyword(s):  
Wastewater Treatment ◽  
Fractal Structure ◽  
Structural Information ◽  
Rapid Determination ◽  
Fractal Dimensions ◽  
Structure Information ◽  
Treatment Processes ◽  
On Line ◽  
Bacterial Aggregates

A rapid method of determining the structure of aggregated particles using small angle laser light scattering is applied here to assemblages of bacteria from wastewater treatment systems. The structure information so obtained is suggestive of fractal behaviour as found by other methods. Strong dependencies are shown to exist between the fractal structure of the bacterial aggregates and the behaviour of the biosolids in zone settling and dewatering by both pressure filtration and centrifugation methods. More rapid settling and significantly higher solids contents are achievable for “looser” flocs characterised by lower fractal dimensions. The rapidity of determination of structural information and the strong dependencies of the effectiveness of a number of wastewater treatment processes on aggregate structure suggests that this method may be particularly useful as an on-line control tool.

FRACTAL DIMENSION, PRIMES, AND THE PERSISTENCE OF MEMORY

2003 ◽  
Vol 06 (02) ◽  
pp. 241-249
Author(s):  
JOSEPH L. PE
Keyword(s):  
Number Theory ◽  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Distinguishing Characteristic ◽  
Local Behavior ◽  
Remarkable Similarity ◽  
Recursive Procedures

Many sequences from number theory, such as the primes, are defined by recursive procedures, often leading to complex local behavior, but also to graphical similarity on different scales — a property that can be analyzed by fractal dimension. This paper computes sample fractal dimensions from the graphs of some number-theoretic functions. It argues for the usefulness of empirical fractal dimension as a distinguishing characteristic of the graph. Also, it notes a remarkable similarity between two apparently unrelated sequences: the persistence of a number, and the memory of a prime. This similarity is quantified using fractal dimension.

scholarly journals Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks

Gels ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 46
Author(s):  
Pedram Nasr ◽  
Hannah Leung ◽  
France-Isabelle Auzanneau ◽  
Michael A. Rogers
Keyword(s):  
Fractal Dimension ◽  
Crystallization Temperature ◽  
Cayley Tree ◽  
Fractal Dimensions ◽  
Self Similarity ◽  
Avrami Model ◽  
Cluster Aggregation ◽  
Box Counting ◽  
Self Assembled ◽  
Limited Diffusion

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.

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