Optimal Taylor-Couette flow: Radius ratio dependence

Taylor-Couette flow with independently rotating inner (i) and outer (o) cylinders is explored numerically and experimentally to determine the effects of the radius ratio {\eta} on the system response. Numerical simulations reach Reynolds numbers of up to Re_i=9.5 x 10^3 and Re_o=5x10^3, corresponding to Taylor numbers of up to Ta=10^8 for four different radius ratios {\eta}=r_i/r_o between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor-Couette (T^3C) setup, reach Reynolds numbers of up to Re_i=2x10^6$ and Re_o=1.5x10^6, corresponding to Ta=5x10^{12} for {\eta}=0.714-0.909. Effective scaling laws for the torque J^{\omega}(Ta) are found, which for sufficiently large driving Ta are independent of the radius ratio {\eta}. As previously reported for {\eta}=0.714, optimum transport at a non-zero Rossby number Ro=r_i|{\omega}_i-{\omega}_o|/[2(r_o-r_i){\omega}_o] is found in both experiments and numerics. Ro_opt is found to depend on the radius ratio and the driving of the system. At a driving in the range between {Ta\sim3\cdot10^8} and {Ta\sim10^{10}}, Ro_opt saturates to an asymptotic {\eta}-dependent value. Theoretical predictions for the asymptotic value of Ro_{opt} are compared to the experimental results, and found to differ notably. Furthermore, the local angular velocity profiles from experiments and numerics are compared, and a link between a flat bulk profile and optimum transport for all radius ratios is reported.Comment: Submitted to JFM, 28 pages, 17 figure

Inter-molecular structure factors of macromolecules in solution: integral equation results

The inter-molecular structure of semidilute polymer solutions is studied theoretically. The low density limit of a generalized Ornstein-Zernicke integral equation approach to polymeric liquids is considered. Scaling laws for the dilute-to-semidilute crossover of random phase (RPA) like structure are derived for the inter-molecular structure factor on large distances when inter-molecular excluded volume is incorporated at the microscopic level. This leads to a non-linear equation for the excluded volume interaction parameter. For macromolecular size-mass scaling exponents, $\nu$, above a spatial-dimension dependent value, $\nu_c=2/d$, mean field like density scaling is recovered, but for $\nu<\nu_c$ the density scaling becomes non-trivial in agreement with field theoretic results and justifying phenomenological extensions of RPA. The structure of the polymer mesh in semidilute solutions is discussed in detail and comparisons with large scale Monte Carlo simulations are added. Finally a new possibility to determine the correction to scaling exponent $\omega_{12}$ is suggested.Comment: 11 pages, 5 figures; to be published in Phys. Rev. E (1999

New Method for Phase transitions in diblock copolymers: The Lamellar case

A new mean-field type theory is proposed to study order-disorder transitions (ODT) in block copolymers. The theory applies to both the weak segregation (WS) and the strong segregation (SS) regimes. A new energy functional is proposed without appealing to the random phase approximation (RPA). We find new terms unaccounted for within RPA. We work out in detail transitions to the lamellar state and compare the method to other existing theories of ODT and numerical simulations. We find good agreements with recent experimental results and predict that the intermediate segregation regime may have more than one scaling behavior.Comment: 23 pages, 8 figure

In silico genotyping of the maize nested association mapping population

Nested Association Mapping (NAM) has been proposed as a means to combine the power of linkage mapping with the resolution of association mapping. It is enabled through sequencing or array genotyping of parental inbred lines while using low-cost, low-density genotyping technologies for their segregating progenies. For purposes of data analyses of NAM populations, parental genotypes at a large number of Single Nucleotide Polymorphic (SNP) loci need to be projected to their segregating progeny. Herein we demonstrate how approximately 0.5 million SNPs that have been genotyped in 26 parental lines of the publicly available maize NAM population can be projected onto their segregating progeny using only 1,106 SNP loci that have been genotyped in both the parents and their 5,000 progeny. The challenge is to estimate both the genotype and genetic location of the parental SNP genotypes in segregating progeny. Both challenges were met by estimating their expected genotypic values conditional on observed flanking markers through the use of both physical and linkage maps. About 90%, of 500,000 genotyped SNPs from the maize HapMap project, were assigned linkage map positions using linear interpolation between the maize Accessioned Gold Path (AGP) and NAM linkage maps. Of these, almost 70% provided high probability estimates of genotypes in almost 5,000 recombinant inbred lines

Prospects for Genomic Selection in Cassava Breeding

Article purchased; Published online: 28 Sept 2017Cassava (Manihot esculenta Crantz) is a clonally propagated staple food crop in the tropics. Genomic selection (GS) has been implemented at three breeding institutions in Africa to reduce cycle times. Initial studies provided promising estimates of predictive abilities. Here, we expand on previous analyses by assessing the accuracy of seven prediction models for seven traits in three prediction scenarios: cross-validation within populations, cross-population prediction and cross-generation prediction. We also evaluated the impact of increasing the training population (TP) size by phenotyping progenies selected either at random or with a genetic algorithm. Cross-validation results were mostly consistent across programs, with nonadditive models predicting of 10% better on average. Cross-population accuracy was generally low (mean = 0.18) but prediction of cassava mosaic disease increased up to 57% in one Nigerian population when data from another related population were combined. Accuracy across generations was poorer than within-generation accuracy, as expected, but accuracy for dry matter content and mosaic disease severity should be sufficient for rapid-cycling GS. Selection of a prediction model made some difference across generations, but increasing TP size was more important. With a genetic algorithm, selection of one-third of progeny could achieve an accuracy equivalent to phenotyping all progeny. We are in the early stages of GS for this crop but the results are promising for some traits. General guidelines that are emerging are that TPs need to continue to grow but phenotyping can be done on a cleverly selected subset of individuals, reducing the overall phenotyping burden

Strategies for implementing genomic selection in family-based aquaculture breeding schemes: double haploid sib test populations

<p>Abstract</p> <p>Background</p> <p>Simulation studies have shown that accuracy and genetic gain are increased in genomic selection schemes compared to traditional aquaculture sib-based schemes. In genomic selection, accuracy of selection can be maximized by increasing the precision of the estimation of SNP effects and by maximizing the relationships between test sibs and candidate sibs. Another means of increasing the accuracy of the estimation of SNP effects is to create individuals in the test population with extreme genotypes. The latter approach was studied here with creation of double haploids and use of non-random mating designs.</p> <p>Methods</p> <p>Six alternative breeding schemes were simulated in which the design of the test population was varied: test sibs inherited maternal (<it>Mat</it>), paternal (<it>Pat</it>) or a mixture of maternal and paternal (<it>MatPat</it>) double haploid genomes or test sibs were obtained by maximum coancestry mating (<it>MaxC</it>), minimum coancestry mating (<it>MinC</it>), or random (<it>RAND</it>) mating. Three thousand test sibs and 3000 candidate sibs were genotyped. The test sibs were recorded for a trait that could not be measured on the candidates and were used to estimate SNP effects. Selection was done by truncation on genome-wide estimated breeding values and 100 individuals were selected as parents each generation, equally divided between both sexes.</p> <p>Results</p> <p>Results showed a 7 to 19% increase in selection accuracy and a 6 to 22% increase in genetic gain in the <it>MatPat</it> scheme compared to the <it>RAND</it> scheme. These increases were greater with lower heritabilities. Among all other scenarios, i.e. <it>Mat, Pat, MaxC</it>, and <it>MinC</it>, no substantial differences in selection accuracy and genetic gain were observed.</p> <p>Conclusions</p> <p>In conclusion, a test population designed with a mixture of paternal and maternal double haploids, i.e. the <it>MatPat</it> scheme, increases substantially the accuracy of selection and genetic gain. This will be particularly interesting for traits that cannot be recorded on the selection candidates and require the use of sib tests, such as disease resistance and meat quality.</p

Response to early generation genomic selection for yield in wheat

We investigated increasing genetic gain for grain yield using early generation genomic selection (GS). A training set of 1,334 elite wheat breeding lines tested over three field seasons was used to generate Genomic Estimated Breeding Values (GEBVs) for grain yield under irrigated conditions applying markers and three different prediction methods: (1) Genomic Best Linear Unbiased Predictor (GBLUP), (2) GBLUP with the imputation of missing genotypic data by Ridge Regression BLUP (rrGBLUP_imp), and (3) Reproducing Kernel Hilbert Space (RKHS) a.k.a. Gaussian Kernel (GK). F2 GEBVs were generated for 1,924 individuals from 38 biparental cross populations between 21 parents selected from the training set. Results showed that F2 GEBVs from the different methods were not correlated. Experiment 1 consisted of selecting F2s with the highest average GEBVs and advancing them to form genomically selected bulks and make intercross populations aiming to combine favorable alleles for yield. F4:6 lines were derived from genomically selected bulks, intercrosses, and conventional breeding methods with similar numbers from each. Results of field-testing for Experiment 1 did not find any difference in yield with genomic compared to conventional selection. Experiment 2 compared the predictive ability of the different GEBV calculation methods in F2 using a set of single plant-derived F2:4 lines from randomly selected F2 plants. Grain yield results from Experiment 2 showed a significant positive correlation between observed yields of F2:4 lines and predicted yield GEBVs of F2 single plants from GK (the predictive ability of 0.248, P < 0.001) and GBLUP (0.195, P < 0.01) but no correlation with rrGBLUP_imp. Results demonstrate the potential for the application of GS in early generations of wheat breeding and the importance of using the appropriate statistical model for GEBV calculation, which may not be the same as the best model for inbreds

Epistasis: Obstacle or Advantage for Mapping Complex Traits?

Identification of genetic loci in complex traits has focused largely on one-dimensional genome scans to search for associations between single markers and the phenotype. There is mounting evidence that locus interactions, or epistasis, are a crucial component of the genetic architecture of biologically relevant traits. However, epistasis is often viewed as a nuisance factor that reduces power for locus detection. Counter to expectations, recent work shows that fitting full models, instead of testing marker main effect and interaction components separately, in exhaustive multi-locus genome scans can have higher power to detect loci when epistasis is present than single-locus scans, and improvement that comes despite a much larger multiple testing alpha-adjustment in such searches. We demonstrate, both theoretically and via simulation, that the expected power to detect loci when fitting full models is often larger when these loci act epistatically than when they act additively. Additionally, we show that the power for single locus detection may be improved in cases of epistasis compared to the additive model. Our exploration of a two step model selection procedure shows that identifying the true model is difficult. However, this difficulty is certainly not exacerbated by the presence of epistasis, on the contrary, in some cases the presence of epistasis can aid in model selection. The impact of allele frequencies on both power and model selection is dramatic

Reproducibility of microvessel counts in breast cancer specimens

Assessment of tumour vascularity in core biopsy specimens may be a useful predictor of response to primary therapy. This study addresses practical methodological issues regarding accuracy of tumour vascularity assessments in different breast cancer specimens. Issues addressed in the study are variation caused by (i) inherent observer variation in the method, (ii) tumour heterogeneity and (iii) previous surgical manipulation of tumours. Microvessel counts were performed by two observers on separate occasions and by two different observers. Counts were performed on core biopsies and tumour sections taken simultaneously (n = 16) and with an intervening time interval (n = 21). In addition core biopsies were obtained from the same tumour on two separate occasions (n = 10). A highly significant correlation was found in counts performed by the same observers at different times and between two different observers. No significant correlation was found in counts of core biopsies and tumour sections taken either simultaneously or subsequently. No correlation was found between counts of sequential core biopsies. Study findings suggest that, although microvessel counts may be assessed reproducibly by the same and different observers, counts performed in core biopsies do not accurately reflect those of overall tumour, limiting their potential as predictive or prognostic markers. © 1999 Cancer Research Campaig