scholarly journals Power-law tails in probability density functions of molecular cloud column density

2015 ◽  
Vol 449 (4) ◽  
pp. 4465-4475 ◽  
Author(s):  
C. M. Brunt
Keyword(s):  
Probability Density ◽  
Power Law ◽  
Molecular Cloud ◽  
Column Density ◽  
Probability Density Functions ◽  
Density Functions

scholarly journals On the extraction of the power-law parts of probability density functions in star-forming clouds

2019 ◽  
Vol 489 (1) ◽  
pp. 788-801 ◽  
Author(s):  
Todor V Veltchev ◽  
Philipp Girichidis ◽  
Sava Donkov ◽  
Nicola Schneider ◽  
Orlin Stanchev ◽  
...  
Keyword(s):  
Probability Density ◽  
Power Law ◽  
Column Density ◽  
Probability Density Functions ◽  
Arbitrary Distribution ◽  
Density Functions ◽  
Theoretical Studies ◽  
Applied Statistics ◽  
New Approach ◽  
Star Forming

ABSTRACT We present a new approach to extract the power-law part of a density/column-density probability density function (ρ-pdf/N-pdf) in star-forming clouds. This approach is based on the mathematical method bPlfit of Virkar & Clauset (2014, Annals of Applied Statistics, 8, 89) and it assesses the power-law part of an arbitrary distribution, without any assumptions about the other parts of this distribution. The slope and deviation point are derived as averaged values as the number of bins is varied. Neither parameter is sensitive to spikes and other local features of the tail. This adapted bPlfit method is applied to two different sets of data from numerical simulations of star-forming clouds at scales 0.5 and 500 pc, and it displays ρ-pdf and N-pdf evolution in agreement with a number of numerical and theoretical studies. Applied to Herschel data on the regions Aquila and Rosette, the method extracts pronounced power-law tails, consistent with those seen in simulations of evolved clouds.

scholarly journals A synergy of the velocity gradients technique and the probability density functions for identifying gravitational collapse in self-absorbing media

2021 ◽  
Vol 502 (2) ◽  
pp. 1768-1784
Author(s):  
Yue Hu ◽  
A Lazarian
Keyword(s):  
Magnetic Fields ◽  
Probability Density ◽  
Column Density ◽  
Mass Density ◽  
Probability Density Functions ◽  
Emission Lines ◽  
Density Functions ◽  
Star Forming ◽  
Velocity Gradients ◽  
Self Gravity

ABSTRACT The velocity gradients technique (VGT) and the probability density functions (PDFs) of mass density are tools to study turbulence, magnetic fields, and self-gravity in molecular clouds. However, self-absorption can significantly make the observed intensity different from the column density structures. In this work, we study the effects of self-absorption on the VGT and the intensity PDFs utilizing three synthetic emission lines of CO isotopologues 12CO (1–0), 13CO (1–0), and C18O (1–0). We confirm that the performance of VGT is insensitive to the radiative transfer effect. We numerically show the possibility of constructing 3D magnetic fields tomography through VGT. We find that the intensity PDFs change their shape from the pure lognormal to a distribution that exhibits a power-law tail depending on the optical depth for supersonic turbulence. We conclude the change of CO isotopologues’ intensity PDFs can be independent of self-gravity, which makes the intensity PDFs less reliable in identifying gravitational collapsing regions. We compute the intensity PDFs for a star-forming region NGC 1333 and find the change of intensity PDFs in observation agrees with our numerical results. The synergy of VGT and the column density PDFs confirms that the self-gravitating gas occupies a large volume in NGC 1333.

Area and volume quantification of arctic thaw slumps using time-series of digital elevation models generated from radar interferometry

2021 ◽  
Author(s):  
Philipp Bernhard ◽  
Simon Zwieback ◽  
Irena Hajnsek
Keyword(s):  
Probability Density ◽  
Power Law ◽  
Volume Change ◽  
Digital Elevation Models ◽  
Probability Density Functions ◽  
The Arctic ◽  
Density Functions ◽  
Digital Elevation ◽  
Beta Coefficient ◽  
Area And Volume

<p>Vast areas of the Arctic host ice-rich permafrost, which is becoming increasingly vulnerable to terrain-altering thermokarst in a warming climate. Among the most rapid and dramatic changes are retrogressive thaw slumps. These slumps evolve by a retreat of the slump headwall during the summer months, making their change visible by comparing digital elevation models over time. In this study we use digital elevation models generated from single-pass radar TanDEM-X observations to derive volume and area change rates for retrogressive thaw slumps. At least three observations in the timespan from 2011 to 2017 are available with a spatial resolution of about 12 meter and a height sensitivity of about 0.5-2 meter. Our study regions include regions in Northern Canada (Peel Plateau/Richardson Mountains, Mackenzie River Delta Uplands, Ellesmere Island), Alaska (Noatak Valley) and Siberia (Yamal, Gydan, Taymyr, Chukotka) covering an area of 220.000 km<sup>2</sup> with a total number of 1853 thaw slumps.</p><p>In this presentation we will focus on the area and volume change rate probability density functions of the mapped thaw slumps in these study areas. For landslides in temperate climate zones the area and volume change probability density function typically follow a distribution that can be characterized by three quantities: A rollover point defined as the peak in the distribution, a cutoff-point indicating the transition to a power law scaling for large landslides and the exponential beta coefficient of this power law. Here we will show that thaw slumps across the arctic follow indeed such a distribution and that the obtained values for the rollover, cutoff and beta coefficient can be used to distinguish between regions. Furthermore we will elaborate on possible reason why arctic thaw slumps can be described by such probability density functions as well as analyzing the differences between regions. This characterization can be useful to further improve our understanding of thaw slump initiation, the investigation of the drivers of their evolution as well as for modeling future thaw slump activity.</p>

scholarly journals Modeling Diameter Distributions with Six Probability Density Functions in Pinus halepensis Mill. Plantations Using Low-Density Airborne Laser Scanning Data in Aragón (Northeast Spain)

2021 ◽  
Vol 13 (12) ◽  
pp. 2307
Author(s):  
J. Javier Gorgoso-Varela ◽  
Rafael Alonso Ponce ◽  
Francisco Rodríguez-Puerta
Keyword(s):  
Probability Density ◽  
Linear Models ◽  
Pinus Halepensis ◽  
Beta Function ◽  
Probability Density Functions ◽  
Lidar Data ◽  
Density Functions ◽  
Minimum Diameter ◽  
Location Parameters ◽  
Diameter Distributions

The diameter distributions of trees in 50 temporary sample plots (TSPs) established in Pinus halepensis Mill. stands were recovered from LiDAR metrics by using six probability density functions (PDFs): the Weibull (2P and 3P), Johnson’s SB, beta, generalized beta and gamma-2P functions. The parameters were recovered from the first and the second moments of the distributions (mean and variance, respectively) by using parameter recovery models (PRM). Linear models were used to predict both moments from LiDAR data. In recovering the functions, the location parameters of the distributions were predetermined as the minimum diameter inventoried, and scale parameters were established as the maximum diameters predicted from LiDAR metrics. The Kolmogorov–Smirnov (KS) statistic (Dn), number of acceptances by the KS test, the Cramér von Misses (W2) statistic, bias and mean square error (MSE) were used to evaluate the goodness of fits. The fits for the six recovered functions were compared with the fits to all measured data from 58 TSPs (LiDAR metrics could only be extracted from 50 of the plots). In the fitting phase, the location parameters were fixed at a suitable value determined according to the forestry literature (0.75·dmin). The linear models used to recover the two moments of the distributions and the maximum diameters determined from LiDAR data were accurate, with R2 values of 0.750, 0.724 and 0.873 for dg, dmed and dmax. Reasonable results were obtained with all six recovered functions. The goodness-of-fit statistics indicated that the beta function was the most accurate, followed by the generalized beta function. The Weibull-3P function provided the poorest fits and the Weibull-2P and Johnson’s SB also yielded poor fits to the data.

scholarly journals Interactive design of probability density functions for shape grammars

2015 ◽  
Vol 34 (6) ◽  
pp. 1-13 ◽  
Author(s):  
Minh Dang ◽  
Stefan Lienhard ◽  
Duygu Ceylan ◽  
Boris Neubert ◽  
Peter Wonka ◽  
...  
Keyword(s):  
Probability Density ◽  
Probability Density Functions ◽  
Interactive Design ◽  
Density Functions ◽  
Shape Grammars

scholarly journals The Impact of Probability Density Functions Assessment on Model Performance for Slope Stability Analysis

Geosciences ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 322
Author(s):  
Evelina Volpe ◽  
Luca Ciabatta ◽  
Diana Salciarini ◽  
Stefania Camici ◽  
Elisabetta Cattoni ◽  
...  
Keyword(s):  
Probability Density ◽  
Central Italy ◽  
Model Performance ◽  
Probability Density Functions ◽  
Slope Instability ◽  
Complex Nature ◽  
Density Functions ◽  
Umbria Region ◽  
Input Variables ◽  
The Impact

The development of forecasting models for the evaluation of potential slope instability after rainfall events represents an important issue for the scientific community. This topic has received considerable impetus due to the climate change effect on territories, as several studies demonstrate that an increase in global warming can significantly influence the landslide activity and stability conditions of natural and artificial slopes. A consolidated approach in evaluating rainfall-induced landslide hazard is based on the integration of rainfall forecasts and physically based (PB) predictive models through deterministic laws. However, considering the complex nature of the processes and the high variability of the random quantities involved, probabilistic approaches are recommended in order to obtain reliable predictions. A crucial aspect of the stochastic approach is represented by the definition of appropriate probability density functions (pdfs) to model the uncertainty of the input variables as this may have an important effect on the evaluation of the probability of failure (PoF). The role of the pdf definition on reliability analysis is discussed through a comparison of PoF maps generated using Monte Carlo (MC) simulations performed over a study area located in the Umbria region of central Italy. The study revealed that the use of uniform pdfs for the random input variables, often considered when a detailed geotechnical characterization for the soil is not available, could be inappropriate.

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