Probability Density Function Analysis Research Articles

Mass classification of dark matter perturbers of stellar tidal streams

Stellar streams formed by tidal stripping of progenitors orbiting around the Milky Way are expected to be perturbed by encounters with dark matter subhalos. Recent studies have shown that they are an excellent proxy to infer properties of the perturbers, such as their mass. Here we present two different methodologies that make use of the fully non-Gaussian density distribution of stellar streams: a Bayesian model selection based on the probability density function (PDF) of stellar density, and a likelihood-free gradient boosting classifier. While the schemes do not assume a specific dark matter model, we are mainly interested in discerning the primordial black holes cold dark matter (PBH CDM) hypothesis form the standard particle dark matter one. Therefore, as an application we forecast model selection strength of evidence for cold dark matter clusters of masses 103–105M⊙ and 105–109M⊙, based on a GD-1-like stellar stream and including realistic observational errors. Evidence for the smaller mass range, so far under-explored, is particularly interesting for PBH CDM. We expect weak to strong evidence for model selection based on the PDF analysis, depending on the fiducial model. Instead, the gradient boosting model is a highly efficient classifier (99% accuracy) for all mass ranges here considered. As a further test of the robustness of the method, we reach similar conclusions when performing forecasts further dividing the largest mass range into 105–107M⊙ and 107–109M⊙ ranges.

Examination of probability distribution of mixture fraction in LES/FDF modelling of a turbulent partially premixed jet flame

An accurate prediction of the probability density function (PDF) of the mixture fraction is crucial to the prediction of combustion since mixing plays an important role in turbulent non-premixed and partially premixed flames. This work provides an assessment of the large-eddy simulation (LES)/filtered density function (FDF) method for the prediction of the PDF of the mixture fraction. The advantage of the LES/FDF method is that it provides the full predictions of the statistical distribution of scalars including the mixture fraction. The predictive accuracy of the method for the PDF is yet to be fully validated. Assessing the prediction of the PDF of the mixture fraction, a conserved scalar, is an important starting point. The Sydney/Sandia inhomogeneous inlet jet flame is used as a test case. A quick comparison shows that the LES/FDF predicted PDF shapes of the mixture fraction deviate significantly from the commonly presumed Beta-PDF as well as from the experimental data in the flame. To examine the source of the discrepancy, we clarify the different PDF definitions used in the comparison among the predictions, measurements, and presumed shape PDFs. The discrepancy observed from the comparison is largely reconciled by clarifying the difference between the PDFs that are examined. The PDF of the resolved mixture fraction is shown to be close to the Beta-PDF in both the measurements and predictions, while the PDF directly deduced from the LES/FDF particles deviates significantly from the Beta-PDF. A multimodal PDF analysis and a pseudo convergence analysis are conducted to provide plausible evidence to support the predicted multimodal PDF shapes. The sub-filter scale FDF is shown to be close to the Beta-PDF too through the construction of a synthesised PDF, which supports the common presumed Beta-PDF assumption used in the presumed PDF methods when combined with LES.

Analysis of wake velocities and pressure fluctuations in a bistable flow using Hilbert–Huang transform and wavelets

This article presents the experimental study of the wake velocity and pressure fluctuations in the bistable flow behind two cylinders side by side. Measurements were conducted in an aerodynamic channel with a pair of cylinders with 25.1 mm of diameter located in the test section, with a pitch-to-diameter ratio p/D of 1.26. The studied Reynolds numbers are Re = 1.61 × 104, Re = 2.16 × 104, and Re = 2.57 × 104, based on the cylinder diameter and the free stream velocity. Pressure fluctuations were measured using condenser microphones positioned in the wake region flush mounted with the upper channel wall. Wake velocity was measured employing hot wire anemometry. Data analysis was performed by Hilbert–Huang transform and by the continuous wavelet transforms, together with a PDF (probability density function) analysis to determine the tools that better represent the phenomena. The results show the presence of the bistable flow in the raw signal; the PDF emphasizes that there is no direct influence of the Reynolds number in the statistical moments, and the JPDFs (joint probability density function) present the bistable variations very clear in the time–frequency relations. The continuous wavelet has high energy under 150 Hz, which can be associated with the vortex shedding. Comparison of the techniques shows that the wavelet transform better represents the bistable signals, allowing the observation of the phenomena and corresponding main frequency ranges. Hilbert–Huang transform shows all the instantaneous frequency modulations present in the signal; the EEMD (Ensemble Empirical Mode Decomposition) represents the most important oscillations of the flow with the identification of the bistable phenomenon. The Hilbert spectra show the location of those oscillations on time and amplitude but cannot identify bistability.

Analysis of Weighted Fractional Fourier Transform Based Hybrid Carrier Signal Characteristics

Recently, a weighted fractional Fourier transform (WFRFT) based hybrid carrier (HC) system has been proposed, which can converge single-carrier (SC) and multi-carrier (MC) systems. The cost and power dissipation of analog components often dominate in practical HC systems. Therefore, in this paper, we analyze the baseband HC signal characteristics, including average signal power, power spectral density (PSD), probability density function (PDF), peak-to-average power ratio (PAPR), and complementary cumulative distribution function (CCDF), using a continuous-time HC signal approximation method. Through theoretical analysis and simulation validation, it is proved that the approximation method does not change the average signal power, bandwidth and out-of-band emission (OOBE). The theoretical PDF expression of HC signal with the approximation method is then proposed. Furthermore, the PDF can also explain why the PAPR of baseband continuous-time HC signal is higher than that of discrete-time HC signal. The PAPR performance and the power amplifier (PA) efficiency of HC systems in different conditions are analyzed. Through the PDF analysis of HC signal envelope and the numerical computations of PAPR, it is shown that the approximation method can offer a precise characteristic description for HC signal, which can help to improve the system PAPR performance and the PA efficiency.

Saharan Dust Events over the Valencian Community (Eastern Iberian Peninsula): Synoptic Circulation Patterns and Contribution to PM10 Levels

ABSTRACT A characterization of Saharan Dust Events (SDE) passing over the Valencian Community (Eastern Spain) during the 2014-2017 period has been carried out. The assessment has focused on the following points: a) the study of their occurrence and impact on PM10 mass concentrations, b) the identification of the favorable synoptic patterns at 850 hPa associated with SDE by means of a cluster analysis and c) the application of the Gamma Probability Density Function (PDF) to fit the mass contributions of SDE to PM10 levels. The study has determined that the Valencian Community (VC) is under the influence of this kind of transport on ~26% of the days of the year, contributing 3.3 mg m-3 (~23%) to the PM10 average value. Five circulation scenarios (1-5) were identified. In scenario 1 (17.4%), the transport was produced due to a trough placed over the southwest of the Iberian Peninsula coupled with a high pressure system centred on Western Algeria, Tunisia and Eastern Libya. According to the PDF analysis, SDE characterized by this type of pattern were most likely to have elevated contributions to PM10 mass concentrations. In scenarios 3 (39.2%) and 5 (19.4%), a high pressure system located over North Africa was present. Both types of patterns also contributed to high concentrations of mineral dust in the VC. Scenarios 1, 3 and 5 were more frequent during summer months, specially type 3 (69%). On the other hand, types 2 (16.2%) and 4 (7.2%), both characterized by a deep low located over the West or Northwest of the Iberian Peninsula, were frequent in spring and, to a lesser extent, during the winter season. Scenarios 2 and 4 had a lower probability to contribute to high concentrations of mineral dust over the study area.

Radio Planetary Nebulae in the Large Magellanic Cloud

We present 21 new radio-continuum detections at catalogued planetary nebula (PN) positions in the Large Magellanic Cloud (LMC) using all presently available data from the Australia Telescope Online Archive at 3, 6, 13 and 20 cm. Additionally, 11 previously detected LMC radio PNe are re-examined with $ 7 $ detections confirmed and reported here. An additional three PNe from our previous surveys are also studied. The last of the 11 previous detections is now classified as a compact \HII\ region which makes for a total sample of 31 radio PNe in the LMC. The radio-surface brightness to diameter ($\Sigma$-D) relation is parametrised as $\Sigma \propto {D^{ - \beta }}$. With the available 6~cm $\Sigma$-$D$ data we construct $\Sigma$-$D$ samples from 28 LMC PNe and 9 Small Magellanic Cloud (SMC) radio detected PNe. The results of our sampled PNe in the Magellanic Clouds (MCs) are comparable to previous measurements of the Galactic PNe. We obtain $\beta=2.9\pm0.4$ for the MC PNe compared to $\beta = 3.1\pm0.4$ for the Galaxy. For a better insight into sample completeness and evolutionary features we reconstruct the $\Sigma$-$D$ data probability density function (PDF). The PDF analysis implies that PNe are not likely to follow linear evolutionary paths. To estimate the significance of sensitivity selection effects we perform a Monte Carlo sensitivity simulation on the $\Sigma$-$D$ data. The results suggest that selection effects are significant for values larger than $\beta \sim 2.6$ and that a measured slope of $\beta=2.9$ should correspond to a sensitivity-free value of $\sim 3.4$.

Classification of Radio Channel disturbances for industrial wireless sensor networks

The reliability of data transmission in Wireless Sensor Networks (WSN) is always an issue in harsh industrial environments and sets specific challenges for performance optimization. Short-term signal disturbances, in the form of multipath fading and destructive radio interference, are of major concern due to signal path conditions (large concrete and metal surfaces), related line-of-sight (LOS) changes (incoming and outgoing trucks, moving around forklifts and workers), and radio frequency interferences. In this paper we introduce the classification procedure where results of Probability Density Function (PDF) analysis and Spectrogram Analysis are combined to classify the measured radio channel disturbances to a set of predefined disturbance classes. The PDF and Spectrogram analysis methods are used for analyzing the statistical properties of the received signal magnitudes. Tracking the changes of the PDF clearly contributes to recognize and characterize the temporal changes, especially LOS changes in the radio link environment. The spectrogram analysis provides additional information of the radio interferences on co- and adjacent channels.