Epipolar Multitarget Velocity Probability Data Association Algorithm Based on the Movement Characteristics of Blasting Fragments

Fragments generated from the blast-fragmentation warhead after blasting are typically multiple, fast, small, and dense. In light of the epipolar multitarget feature of blasting fragments, this paper utilizes the movement characteristics of blasting fragments for modeling. Then, the modeling results are adopted in probabilistic data association (PDA) algorithm of multitarget tracking. A novel epipolar multitarget velocity PDA (VPDA) algorithm is proposed based on the movement characteristics of blasting fragments. This algorithm forms the movement characteristics with the finite element simulation results of warhead blasting fragments, utilizes the Doppler velocity probability to reassign the association probability, and updates the state and covariance of each target through the probability weighted fusion. Simulation results demonstrate that, the computational complexity of the proposed algorithm is close to that of PDA algorithm, and the association success rate and the state value update error approximates to the association effects of joint probabilistic data association (JPDA) algorithm, which can effectively track the fragments with identical velocity while reducing the complexity of the epipolar multitarget tracking algorithm, and can respond to the group target tracking scenario.

Statistical deprojection of intervelocities, interdistances, and masses in the Isolated Galaxy Pair Catalog

Aims. In order to study the internal dynamics of actual galaxy pairs, we need to derive the probability distribution function (PDF) of true 3D, orbital intervelocities and interdistances between pair members from their observed projected values along with the pair masses from Kepler’s third law. For this research, we used 13 114 pairs from the Isolated Galaxy Pair Catalog (IGPC). Methods. The algorithms of statistical deprojection previously elaborated were applied to these observational data. We derived the orbital velocity PDFs for the whole catalog and for several selected subsamples. The interdistance PDF is deprojected and compared to the analytical profiles expected from semi-theoretical arguments. Results. The PDF of deprojected pair orbital velocities is characterized by the existence of a main probability peak around ≈150 km s−1 for all subsamples of the IGPC as well as for the Uppsala Galaxy Pair Catalog. The interdistance PDFs of both the projected and deprojected data are described at large distances by the same power law with exponent ≈ − 2. The whole distributions, including their cores, are fairly fitted by King profiles. The mass deprojection yields a mass/luminosity ratio for the pairs of M/L = (30 ± 5) in solar units. Conclusions. The orbital velocity probability peak is observed at the same value, ≈150 km s−1, as the main exoplanet velocity peak, which points toward a possible universality of Keplerian structures, whatever the scale. The pair M/L ratio is just seven times the standard ratio for luminous matter, which does not require the existence of nonbaryonic dark matter in these systems.

Uncertainty Rank for Streamline Ensembles

Traditional spaghetti plots from ensemble data provide no explicit information as to the uncertainty of the realization flow paths. While intuitive assessment can be used when visualizing streamline density directly in such a plot, the display is often cluttered and difficult to interpret. The authors present a method to measure uncertainty and visualize member streamlines from an ensemble of vector fields. The method incorporates velocity probability density as a feature along each member streamline. The authors show visualizations of two different data sets using the proposed method.

An Improved Double-Gaussian Closure for the Subgrid Vertical Velocity Probability Distribution Function

The vertical velocity probability distribution function (PDF) is analyzed throughout the depth of the lower atmosphere, including the subcloud and cloud layers, in four large-eddy simulation (LES) cases of shallow cumulus and stratocumulus. Double-Gaussian PDF closures are examined to test their ability to represent a wide range of turbulence statistics, from stratocumulus cloud layers characterized by Gaussian turbulence to shallow cumulus cloud layers displaying strongly non-Gaussian turbulence statistics. While the majority of the model closures are found to perform well in the former case, the latter presents a considerable challenge. A new model closure is suggested that accounts for high skewness and kurtosis seen in shallow cumulus cloud layers. The well-established parabolic relationship between skewness and kurtosis is examined, with results in agreement with previous studies for the subcloud layer. In cumulus cloud layers, however, a modified relationship is necessary to improve performance. The new closure significantly improves the estimation of the vertical velocity PDF for shallow cumulus cloud layers, in addition to performing well for stratocumulus. In particular, the long updraft tail representing the bulk of cloudy points is much better represented and higher-order moments diagnosed from the PDF are also greatly improved. However, some deficiencies remain owing to fundamental limitations of representing highly non-Gaussian turbulence statistics with a double-Gaussian PDF.

Scale matters

The applicability of Navier–Stokes equations is limited to near-equilibrium flows in which the gradients of density, velocity and energy are small. Here I propose an extension of the Chapman–Enskog approximation in which the velocity probability distribution function (PDF) is averaged in the coordinate phase space as well as the velocity phase space. I derive a PDF that depends on the gradients and represents a first-order generalization of local thermodynamic equilibrium. I then integrate this PDF to derive a hydrodynamic model. I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics. This article is part of the theme issue ‘Hilbert’s sixth problem’.

Is the Link Between the Observed Velocities of Neutron Stars and their Progenitors a Simple Mass Relationship?

While the imparting of velocity ‘kicks’ to compact remnants from supernovae is widely accepted, the relationship of the ‘kick’ to the progenitor is not. We propose the ‘kick’ is predominantly a result of conservation of momentum between the ejected and compact remnant masses. We propose the ‘kick’ velocity is given by vkick = α(Mejecta/Mremnant)+β, where α and β are constants we wish to determine. To test this we use the BPASS v2 (Binary Population and Spectral Synthesis) code to create stellar populations from both single star and binary star evolutionary pathways. We then use our Remnant Ejecta and Progenitor Explosion Relationship (REAPER) code to apply ‘kicks’ to neutron stars from supernovae in these models using a grid of α and β values, (from 0 to 200 km s−1 in steps of 10 km s−1), in three different ‘kick’ orientations, (isotropic, spin-axis aligned and orthogonal to spin-axis) and weighted by three different Salpeter initial mass functions (IMF’s), with slopes of -2.0, -2.35 and -2.70. We compare our synthetic 2D and 3D velocity probability distributions to the distributions provided by Hobbs et al. (1995).

An Undersea Mining Microseism Source Location Algorithm Considering Wave Velocity Probability Distribution

The traditional mine microseism locating methods are mainly based on the assumption that the wave velocity is uniform through the space, which leads to some errors for the assumption goes against the laws of nature. In this paper, the wave velocity is regarded as a random variable, and the probability distribution information of the wave velocity is fused into the traditional locating method. This paper puts forwards the microseism source location method for the undersea mining on condition of the probability distribution of the wave velocity and comes up with the solving process of Monte Carlo. In addition, based on the simulated results of the Monte Carlo method, the space is divided into three areas: the most possible area (area I), the possible area (area II), and the small probability area (area III). Attached to corresponding mathematical formulations, spherical models and cylindrical models in different areas are, respectively, built according to whether the source is in the sensor arrays. Both the examples and the actual applications show that (1) the method of microseism source location in this paper can highly improve the accuracy of the microseism monitoring, especially for the source beyond the sensor arrays, and (2) the space-dividing method based on occurrence possibilities of the source can recognize and sweep the hidden dangers for it predicts the probable location range of the source efficiently, while the traditional method cannot.