Experimental investigation of scalar-scalar-dissipation filtered joint density function and its transport equation

2003 ◽  
Vol 15 (1) ◽  
pp. 227-244 ◽  
Author(s):  
Anand G. Rajagopalan ◽  
Chenning Tong
Keyword(s):  
Experimental Investigation ◽  
Transport Equation ◽  
Density Function ◽  
Joint Density ◽  
Scalar Dissipation ◽  
Joint Density Function

scholarly journals Comparison of models for missing pedigree in single-step genomic prediction

2021 ◽  
Vol 99 (2) ◽  
Author(s):  
Yutaka Masuda ◽  
Shogo Tsuruta ◽  
Matias Bermann ◽  
Heather L Bradford ◽  
Ignacy Misztal
Keyword(s):  
Density Function ◽  
Single Step ◽  
Joint Density ◽  
Pedigree Information ◽  
Relationship Matrix ◽  
Genomic Information ◽  
Breeding Values ◽  
Joint Density Function ◽  
Information Updates ◽  
Genetic Trends

Abstract Pedigree information is often missing for some animals in a breeding program. Unknown-parent groups (UPGs) are assigned to the missing parents to avoid biased genetic evaluations. Although the use of UPGs is well established for the pedigree model, it is unclear how UPGs are integrated into the inverse of the unified relationship matrix (H-inverse) required for single-step genomic best linear unbiased prediction. A generalization of the UPG model is the metafounder (MF) model. The objectives of this study were to derive 3 H-inverses and to compare genetic trends among models with UPG and MF H-inverses using a simulated purebred population. All inverses were derived using the joint density function of the random breeding values and genetic groups. The breeding values of genotyped animals (u2) were assumed to be adjusted for UPG effects (g) using matrix Q2 as u2∗=u2+Q2g before incorporating genomic information. The Quaas–Pollak-transformed (QP) H-inverse was derived using a joint density function of u2∗ and g updated with genomic information and assuming nonzero cov(u2∗,g′). The modified QP (altered) H-inverse also assumes that the genomic information updates u2∗ and g, but cov(u2∗,g′)=0. The UPG-encapsulated (EUPG) H-inverse assumed genomic information updates the distribution of u2∗. The EUPG H-inverse had the same structure as the MF H-inverse. Fifty percent of the genotyped females in the simulation had a missing dam, and missing parents were replaced with UPGs by generation. The simulation study indicated that u2∗ and g in models using the QP and altered H-inverses may be inseparable leading to potential biases in genetic trends. Models using the EUPG and MF H-inverses showed no genetic trend biases. These 2 H-inverses yielded the same genomic EBV (GEBV). The predictive ability and inflation of GEBVs from young genotyped animals were nearly identical among models using the QP, altered, EUPG, and MF H-inverses. Although the choice of H-inverse in real applications with enough data may not result in biased genetic trends, the EUPG and MF H-inverses are to be preferred because of theoretical justification and possibility to reduce biases.

Experimental investigation of dissipation-element statistics in scalar fields of a jet flow

2013 ◽  
Vol 724 ◽  
pp. 337-366 ◽  
Author(s):  
Markus Gampert ◽  
Philip Schaefer ◽  
Norbert Peters
Keyword(s):  
Experimental Investigation ◽  
Scalar Field ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Dissipation Rate ◽  
Scalar Dissipation ◽  
Streamwise Direction ◽  
Scalar Dissipation Rate ◽  
Dissipation Elements

AbstractWe present a detailed experimental investigation of conditional statistics obtained from dissipation elements based on the passive scalar field$\theta $and its instantaneous scalar dissipation rate$\chi $. Using high-frequency planar Rayleigh scattering measurements of propane discharging as a round turbulent jet into coflowing carbon dioxide, we acquire with Taylor’s hypothesis a highly resolved three-dimensional field of the propane mass fraction$\theta $. The Reynolds number (based on nozzle diameter and jet exit velocity) varies between 3000 and 8600. The experimental results for the joint probability density of the scalar difference$ \mathrm{\Delta} \theta $and the length$l$of dissipation elements resembles those previously obtained from direct numerical simulations of Wang & Peters (J. Fluid Mech., vol. 554, 2006, pp. 457–475). In addition, the normalized marginal probability density function$\tilde {P} (\tilde {l} )$of the length of dissipation elements follows closely the theoretical model derived by Wang & Peters (J. Fluid Mech., vol. 608, 2008, pp. 113–138). We also find that the mean linear distance${l}_{m} $between two extreme points of an element is of the order of the scalar Taylor microscale${\lambda }_{u} $. Furthermore, the conditional mean$\langle \mathrm{\Delta} \theta \vert l\rangle $scales with Kolmogorov’s$1/ 3$power law. The investigation of the orientation of long dissipation elements in the jet flow reveals a preferential alignment, perpendicular to the streamwise direction for long elements, while the orientation of short elements is close to isotropic. Following an approach proposed by Kholmyansky & Tsinober (Phys. Lett. A, vol. 373, 2009, pp. 2364–2367), we finally investigate the probability density function of the scalar increment$\delta \theta $in the streamwise direction, when strong dissipative events are either retained in or excluded from the measurement volume. In the present study, however, these events are related to maximum points of the scalar dissipation rate$\chi $together with their local extent. When these regions are excluded from the scalar field, we observe a tendency of the probability density function$P(\delta \theta (r))$towards a Gaussian bell-shaped curve.

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