Fractal statistics in young star clusters: structural parameters and dynamical evolution

ABSTRACT We used fractal statistics to quantify the degree of observed substructures in a sample of 50 embedded clusters and more evolved open clusters (< 100 Myr) found in different galactic regions. The observed fractal parameters were compared with N-body simulations from the literature, which reproduce star-forming regions under different initial conditions and geometries that are related to the cluster's dynamical evolution. Parallax and proper motion from Gaia-DR2 were used to accurately determine cluster membership by using the Bayesian model and cross-entropy technique. The statistical parameters $\mathcal {Q}$, $\overline{m}$ and $\overline{s}$ were used to compare observed cluster structure with simulations. A low level of substructures ($\mathcal {Q} \lt $ 0.8) is found for most of the sample that coincides with simulations of regions showing fractal dimension D ∼ 2–3. Few clusters (<20 per cent) have uniform distribution with a radial density profile (α < 2). A comparison of $\mathcal {Q}$ with mass segregation (ΛMSR) and local density as a function of mass (ΣLDR) shows the clusters coinciding with models that adopt supervirial initial conditions. The age–crossing time plot indicates that our objects are dynamically young, similar to the unbound associations found in the Milky Way. We conclude that this sample may be expanding very slowly. The flat distribution in the $\mathcal {Q}$–age plot and the absence of trends in the distributions of ΛMSR and ΣLDR against age show that in the first 10 Myr the clusters did not change structurally and seem not to have expanded from a much denser region.

Formation, Initial Evolution and Galactic Dynamic Evolution of Young Star Clusters

We present an analysis of a sample of clusters of young stars in order to investigate the inherent properties of clustering and dynamic evolution of stellar components, based on fractal statistics. In addition, we present the application of new mathematical and numerical techniques with potentiality for use in models of filamentary structures.

Philippine Poverty as Moving Fractals

A recent innovation in the field of statistics is using fractal analysis where data sets are analyzed for anomaly detection, pattern analysis, and root cause analysis. In application of the fractal statistics, this paper examines the incidence of Philippine poverty from 2003 to 2012 based on its fractal dimension in the hope of providing policy makers a different approach in addressing sustained growth among the poor. Poverty is like a moving fractal where patterns simply repeat in various scales and variations. What are the key implications of fractal poverty for policy and research? How can the fractal poverty provide an analytical foundation to make a pathway out of poverty accessible to Filipinos presently suffering in extreme poverty? The fractal model shows that poverty incidence is dictated by provinces whose poverty incidence are high. This means that if the poverty incidence of the province will be primarily addressed, it will affect the poverty scenario of the Philippines. Policy makers if looking for key indicators why Filipinos have some difficulty escaping poverty may focus on the province with the highest incidence.

VARIATIONS OF SLOPE OF AN EARTHQUAKE RECURRENCE CURVE IN MINGYACHEVIR RESERVOIR ZONE

Изучена величина наклона графика повторяемости (при использовании магнитудной шкалы), отра- жающая распределение числа землетрясений по их энергии и широко используемая для характеристики сейсмического процесса. По данным каталогов РЦСС НАНА были выбраны землетрясения, относящиеся к зоне Мингячевирского водохранилища за период 1935-2002 и 2003-2014 гг. Исследованы изменения величины наклона графика повторяемости землетрясений во времени для зоны Мингячевирского водо- хранилища. Проведены исследования по фрактальной статистике землетрясений в зоне Мингячевирского водохранилища, а также построена карта сейсмической активности за последние 10 лет Value of slope of a recurrence curve which shows earthquakes number distribution on their energy and which is widely used for seismic process characteristics was studied (with the help of a magnitude scale). Earthquakes referred to Mingyachevir reservoir zone for the time period 19352002 and 20032014 have been chosen by the data of RCSS ANAS catalogues. Time variations of slope of an earthquake recurrence curve value were investigated for Mingyachevir reservoir zone. Investigations on the basis of fractal statistics of the earthquakes in the given zone were carried out and the map of seismic activity for a period of past 10 years was made

Development Features and Fractal Research of Fault Structure of No.5 Coal Seam in Chenghe-Second Coal Mine

Based on the collected geological exploration and underground mining data, this thesis has analyzed the development feature of faults of No.5 coal seam in Chenghe-Second coal mine and obtained fractal law of fault structure by fractal statistics. The result shows that the faults have a good self-similarity on the plane distribution and obvious fractal characteristics and that the larger the fractal dimension, the higher the complex degree of fault structures.

ON ALLOMETRY RELATIONS

There are a substantial number of empirical relations that began with the identification of a pattern in data; were shown to have a terse power-law description; were interpreted using existing theory; reached the level of "law" and given a name; only to be subsequently fade away when it proved impossible to connect the "law" with a larger body of theory and/or data. Various forms of allometry relations (ARs) have followed this path. The ARs in biology are nearly two hundred years old and those in ecology, geophysics, physiology and other areas of investigation are not that much younger. In general if X is a measure of the size of a complex host network and Y is a property of a complex subnetwork embedded within the host network a theoretical AR exists between the two when Y = aXb. We emphasize that the reductionistic models of AR interpret X and Y as dynamic variables, albeit the ARs themselves are explicitly time independent even though in some cases the parameter values change over time. On the other hand, the phenomenological models of AR are based on the statistical analysis of data and interpret X and Y as averages to yield the empirical AR: 〈Y〉 = a〈X〉b. Modern explanations of AR begin with the application of fractal geometry and fractal statistics to scaling phenomena. The detailed application of fractal geometry to the explanation of theoretical ARs in living networks is slightly more than a decade old and although well received it has not been universally accepted. An alternate perspective is given by the empirical AR that is derived using linear regression analysis of fluctuating data sets. We emphasize that the theoretical and empirical ARs are not the same and review theories "explaining" AR from both the reductionist and statistical fractal perspectives. The probability calculus is used to systematically incorporate both views into a single modeling strategy. We conclude that the empirical AR is entailed by the scaling behavior of the probability density, which is derived using the probability calculus.