scholarly journals A new view of flow topology and conditional statistics in turbulence

2013 ◽  
Vol 371 (1982) ◽  
pp. 20120169 ◽  
Author(s):  
Lipo Wang ◽  
Norbert Peters
Keyword(s):  
Joint Probability ◽  
Shape Parameters ◽  
Flow Topology ◽  
Velocity Derivative ◽  
Conditional Statistics ◽  
Dissipation Elements ◽  
The Given ◽  
Relevant Work ◽  
Joint Probability Density ◽  
Tube Segment

By partitioning a turbulent flow field into relative simple units, the original complex system may be better understood from studying decomposed structures. In this paper, some general principles for identifying geometrical decomposition are discussed. Logically, to make analysis more objective and quantitative, the decomposed units need to be non-arbitrarily defined and space filling. Following this vein, we introduced two topological approaches satisfying these prerequisites and the relevant work is reviewed. For a given scalar variable, dissipation elements are defined as the spatial regions that the gradient trajectories of this scalar can share the same pair of scalar extremums (one maximum and one minimum), whereas for the general vector variables, vector tube segments are the part of vector tubes bounded by adjacent extremums of the magnitude of the given vector. Both structures can be characterized by representative shape parameters: the length scale and the extremum difference. On the basis of direct numerical simulation data, the statistics of the shape parameters have been studied. Physically, those structures reveal the ‘nature’ topology of turbulence, and thus their characteristic parameters reflect the flow properties. For instance, when the vector tube segment approach is applied to the velocity case, the negative skewness of the velocity derivative can be explained by the asymmetry of the joint probability density function of the shape parameters of streamtube segments. Conditional statistics based on these newly defined structures identify finer flow physics and are believed helpful for modelling improvement. Application examples illustrate that, in principle, these methods can generally be applied to different flow cases under different situations.

scholarly journals Plane Partitions in Batch Track-Track Associations

2020 ◽  
Author(s):  
C Nelatury
Keyword(s):  
Autonomous Vehicles ◽  
Joint Probability ◽  
Geometric Approach ◽  
Multiple Target Tracking ◽  
Multiple Sensors ◽  
Track Association ◽  
Output Characteristics ◽  
Sweep Line ◽  
Joint Probability Density ◽  
Vital Factor

The most difficult multiple target tracking problem includes multiple sensors with different viewing angles, measurement geometries, fields of view, accuracies, resolutions and scan rates. Such variations in sensor output characteristics as well as channel delays, countermeasures, inherent target features and maneuvers have solidified the consensus that an effective fusion system must handle several levels of “tracklets” from distributed sources in order to produce the desired long tracks as described in Waltz and Llinas (1990). In view of the increased attention given to hypersonics as well as the increased need for low-level signal processing, the computational complexity of track association is a vital factor in determining an autonomous vehicles’ ability to complete its objectives quickly. We are given a set of tracklets where the particular methods used to make the detections are taken for granted. Following joint probability density association filters, we assume short tracklets are completed (i.e, detections are correctly correlated with state estimates) and take a computational geometric approach to associating tracklets. If N is the number of short term tracklets, this method fuses them in O(N2). Using covariance as a distance, this report suggests the applicability of a class of sweep-line algorithms developed in computational geometry in data fusion.

scholarly journals Analysis of COSIMA spectra: Bayesian approach

2015 ◽  
Vol 4 (1) ◽  
pp. 139-148
Author(s):  
H. J. Lehto ◽  
B. Zaprudin ◽  
K. M. Lehto ◽  
T. Lönnberg ◽  
J. Silén ◽  
...  
Keyword(s):  
Mass Spectra ◽  
Joint Probability ◽  
Mass Analyzer ◽  
Mass Scaling ◽  
Tof Sims ◽  
Analysis Methods ◽  
Measured Line ◽  
Complex Forms ◽  
Joint Probability Density ◽  
Secondary Ion

Abstract. We describe the use of Bayesian analysis methods applied to time-of-flight secondary ion mass spectrometer (TOF-SIMS) spectra. The method is applied to the COmetary Secondary Ion Mass Analyzer (COSIMA) TOF-SIMS mass spectra where the analysis can be broken into subgroups of lines close to integer mass values. The effects of the instrumental dead time are discussed in a new way. The method finds the joint probability density functions of measured line parameters (number of lines, and their widths, peak amplitudes, integrated amplitudes and positions). In the case of two or more lines, these distributions can take complex forms. The derived line parameters can be used to further calibrate the mass scaling of TOF-SIMS and to feed the results into other analysis methods such as multivariate analyses of spectra. We intend to use the method, first as a comprehensive tool to perform quantitative analysis of spectra, and second as a fast tool for studying interesting targets for obtaining additional TOF-SIMS measurements of the sample, a property unique to COSIMA. Finally, we point out that the Bayesian method can be thought of as a means to solve inverse problems but with forward calculations, only with no iterative corrections or other manipulation of the observed data.

scholarly journals Modeling of Future Extreme Storm Surges at the NW Mediterranean Coast (Spain)

Water ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 472
Author(s):  
Jue Lin-Ye ◽  
Manuel García-León ◽  
Vicente Gràcia ◽  
María Ortego ◽  
Piero Lionello ◽  
...  
Keyword(s):  
Probability Density ◽  
Large Scale ◽  
Joint Probability ◽  
Storm Surges ◽  
Additive Models ◽  
Change Scenario ◽  
Event Duration ◽  
Extreme Storm ◽  
Climate Patterns ◽  
Joint Probability Density

Storm surges are one of the main drivers for extreme flooding at the coastal areas. Such events can be characterized with the maximum level in an extreme storm surge event (surge peak), as well as the duration of the event. Surge projections come from a barotropic model for the 1950–2100 period, under a severe climate change scenario (RCP 8.5) at the northeastern Spanish coast. The relationship of extreme storm surges to three large-scale climate patterns was assessed: North Atlantic Oscillation ( N A O ), East Atlantic Pattern ( E A W R ), and Scandinavian Pattern ( S C ). The statistical model was built using two different strategies. In Strategy #1, the joint probability density was characterized by a moving-average series of stationary Archimedean copula, whereas in Strategy #2, the joint probability density was characterized by a non-stationary probit copula. The parameters of the marginal distribution and the copula were defined with generalized additive models. The analysis showed that the mean values of surge peak and event duration were constant and were independent of the proposed climate patterns. However, the values of N A O and S C influenced the threshold and the storminess of extreme events. According to Strategy #1, the variance of the surge peak and event duration increased with a fast shift of negative S C and a positive N A O , respectively. Alternatively, Strategy #2 showed that the variance of the surge peak increased with a positive E A W R . Both strategies coincided in that the joint dependence of the maximum surge level and the duration of extreme surges ranged from low to medium degree. Its mean value was stationary, and its variability was linked to the geographical location. Finally, Strategy #2 helped determine that this dependence increased with negative N A O .

scholarly journals Statistics for Ratios of Rayleigh, Rician, Nakagami-m, and Weibull Distributed Random Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Dragana Č. Pavlović ◽  
Nikola M. Sekulović ◽  
Gradimir V. Milovanović ◽  
Aleksandra S. Panajotović ◽  
Mihajlo Č. Stefanović ◽  
...  
Keyword(s):  
Random Variables ◽  
Joint Probability ◽  
Wireless Systems ◽  
Technical Literature ◽  
Product Moments ◽  
Outdoor Environments ◽  
Indoor And Outdoor Environments ◽  
Analytical Expressions ◽  
Joint Probability Density ◽  
Indoor And Outdoor

The distributions of ratios of random variables are of interest in many areas of the sciences. In this brief paper, we present the joint probability density function (PDF) and PDF of maximum of ratiosμ1=R1/r1andμ2=R2/r2for the cases whereR1,R2,r1, andr2are Rayleigh, Rician, Nakagami-m, and Weibull distributed random variables. Random variablesR1andR2, as well as random variablesr1andr2, are correlated. Ascertaining on the suitability of the Weibull distribution to describe fading in both indoor and outdoor environments, special attention is dedicated to the case of Weibull random variables. For this case, analytical expressions for the joint PDF, PDF of maximum, PDF of minimum, and product moments of arbitrary number of ratiosμi=Ri/ri,i=1,…,Lare obtained. Random variables in numerator,Ri, as well as random variables in denominator,ri, are exponentially correlated. To the best of the authors' knowledge, analytical expressions for the PDF of minimum and product moments of{μi}i=1Lare novel in the open technical literature. The proposed mathematical analysis is complemented by various numerical results. An application of presented theoretical results is illustrated with respect to performance assessment of wireless systems.

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