Elliptic flow in transport theory and hydrodynamics

We present a new direct simulation Monte-Carlo method for solving the relativistic Boltzmann equation. We solve numerically the 2-dimensional Boltzmann equation using this new algorithm. We find that elliptic flow from this transport calculation smoothly converges towards the value from ideal hydrodynamics as the number of collisions per particle increases, as expected on general theoretical grounds, but in contrast with previous transport calculations.Comment: 5 pages, 3 figures, revise

Derivation of the Lattice Boltzmann Model for Relativistic Hydrodynamics

A detailed derivation of the Lattice Boltzmann (LB) scheme for relativistic fluids recently proposed in Ref. [1], is presented. The method is numerically validated and applied to the case of two quite different relativistic fluid dynamic problems, namely shock-wave propagation in quark-gluon plasmas and the impact of a supernova blast-wave on massive interstellar clouds. Close to second order convergence with the grid resolution, as well as linear dependence of computational time on the number of grid points and time-steps, are reported

Genomics for the advancement of livestock production: A South African perspective

Most of the growth of human populations worldwide will be in developing countries, including South Africa. Natural resources are under immense pressure and animal scientists are faced with the challenges for increased efficiency and long-term sustainability of livestock production. Since the completion of the Human Genome Project, animal genomes have been mapped with genomics, enabling new opportunities for application in farm animal species. The use of microsatellite markers has made significant contributions to the insight in genetic characterisation of indigenous and local developed breeds in most farm species in South Africa and Africa. The single nucleotide polymorphic (SNP) marker discovery and development of commercial SNP arrays made genomic selection possible and genomic enhanced breeding values (GEBVs) are used widely in the First World. In South Africa, genomic programmes for beef and dairy cattle were established in 2015 and 2016, with the focus on building training populations for genomic selection. The SA Bonsmara breed was the first to receive GEBV. The availability of hard-to-measure phenotypes is limited, and these are the traits that hold the most potential for genomic selection and answering to the challenges of methane (CH4) emissions and higher efficiency. Genome editing, which involves zinc-finger nucleases (ZFNs), transcription-activators such as endonucleases (TALEN) and RNA-programmable genome editor (CRISPR/CAS9), includes the most recent technology for application in precision genetics. Welfare and ethical concerns will be an important consideration in the acceptability of genome editing to consumers. Applications that benefit the animals are more acceptable to the public. The use of genome editing to produce polled cattle is one of the first applications with a direct welfare impact as it nullifies the need for painful dehorning. In this paper, genomic technology is reviewed with the focus on the most recent research trends and commercial application of genomics towards the genetic improvement of livestock with specific reference to South Africa.Keywords: Genetic diversity, genomic selection, gene editing, microsatellite markers, SN

Genetic polymorphism of CSN1S2 in South African dairy goat populations

Alpha-s2 casein has a significant influence on protein content in goat milk, and the technological properties important for cheese processing. Specific alleles (A, B, C, E and F) of the alpha (α)s2-casein gene (CSN1S2) result in higher protein, casein and fat content, and improved coagulation properties, which are useful for improved cheese making. The aim of this study was to investigate the polymorphism and genetic variation of CSN1S2 in South African dairy goats, using DNA sequencing technology. Sixty dairy goats (20 Saanes, 20 British Alpine, and 20 Toggenburg) and 20 meat-type goats were sequenced with four primers to distinguish among the seven known alleles for αs2-casein. A total of four alleles (A, B, C and F) for CSN1S2 were observed among the dairy- and meat-type populations with ten genotypes across the populations. The A allele and the AA genotype were the most frequent across the populations, with the favourable AC genotype being the most frequent (0.300) in the Saanen population. Two unique genotypes were detected in the Toggenburg (BB and BF) and one in the meat-type goats (CF). The results indicate moderate genetic variation for αs2-casein in the South African goat populations (42.3–63.6%). Low positive FST values suggest limited inbreeding. This study confirmed the presence of favourable alleles in the South African goat populations, indicating room for genetic improvement using directional selection for favourable genotypes.Keywords: alpha-s2-casein, genetic variation, goat milk, protein content, Saane

On the hyperbolicity and causality of the relativistic Euler system under the kinetic equation of state

We show that a pair of conjectures raised in [11] concerning the construction of normal solutions to the relativistic Boltzmann equation are valid. This ensures that the results in [11] hold for any range of positive temperatures and that the relativistic Euler system under the kinetic equation of state is hyperbolic and the speed of sound cannot overcome $c/\sqrt{3}$.Comment: 6 pages. Abridged version; full version to appear in Commun. Pure Appl. Ana

Linking the hydrodynamic and kinetic description of a dissipative relativistic conformal theory

We use the entropy production variational method to associate a one particle distribution function to the assumed known energy-momentum and entropy currents describing a relativistic conformal fluid. Assuming a simple form for the collision operator we find this one particle distribution function explicitly, and show that this method of linking the hydro and kinetic description is a non trivial generalization of Grad's ansatz. The resulting constitutive relations are the same as in the conformal dissipative type theories discussed in J. Peralta-Ramos and E. Calzetta, Phys. Rev. D {\bfseries 80}, 126002 (2009). Our results may prove useful in the description of freeze-out in ultrarelativistic heavy-ion collisions.Comment: v2: 23 pages, no figures, accepted in Phys. Rev.

Semitoric integrable systems on symplectic 4-manifolds

Let M be a symplectic 4-manifold. A semitoric integrable system on M is a pair of real-valued smooth functions J, H on M for which J generates a Hamiltonian S^1-action and the Poisson brackets {J,H} vanish. We shall introduce new global symplectic invariants for these systems; some of these invariants encode topological or geometric aspects, while others encode analytical information about the singularities and how they stand with respect to the system. Our goal is to prove that a semitoric system is completely determined by the invariants we introduce

Derivation of transient relativistic fluid dynamics from the Boltzmann equation

In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional 14-moment approximation is that we will not close the fluid-dynamical equations of motion by truncating the expansion of the distribution function. Instead, we keep all terms in the moment expansion. The reduction of the degrees of freedom is done by identifying the microscopic time scales of the Boltzmann equation and considering only the slowest ones. In addition, the equations of motion for the dissipative quantities are truncated according to a systematic power-counting scheme in Knudsen and inverse Reynolds number. We conclude that the equations of motion can be closed in terms of only 14 dynamical variables, as long as we only keep terms of second order in Knudsen and/or inverse Reynolds number. We show that, even though the equations of motion are closed in terms of these 14 fields, the transport coefficients carry information about all the moments of the distribution function. In this way, we can show that the particle-diffusion and shear-viscosity coefficients agree with the values given by the Chapman-Enskog expansion.Comment: 27 page

Genetic diversity and population structure among six cattle breeds in South Africa using a whole genome SNP panel

Information about genetic diversity and population structure among cattle breeds is essential for genetic improvement, understanding of environmental adaptation as well as utilization and conservation of cattle breeds. This study investigated genetic diversity and the population structure among six cattle breeds in South African (SA) including Afrikaner (n=44), Nguni (n=54), Drakensberger (n=47), Bonsmara (n=44), Angus (n=31) and Holstein (n=29). Genetic diversity within cattle breeds was analyzed using three measures of genetic diversity namely allelic richness (AR), expected heterozygosity (He) and inbreeding coefficient (f). Genetic distances between breed pairs were evaluated using Nei’s genetic distance. Population structure was assessed using model-based clustering (ADMIXTURE). Results of this study revealed that the allelic richness ranged from 1.88 (Afrikaner) to 1.73 (Nguni). Afrikaner cattle had the lowest level of genetic diversity (He=0.24) and the Drakensberger cattle (He=0.30) had the highest level of genetic variation among indigenous and locally-developed cattle breeds. The level of inbreeding was lower across the studied cattle breeds. As expected the average genetic distance was the greatest between indigenous cattle breeds and Bos taurus cattle breeds but the lowest among indigenous and locally-developed breeds. Model-based clustering revealed some level of admixture among indigenous and locally-developed breeds and supported the clustering of the breeds according to their history of origin. The results of this study provided useful insight regarding genetic structure of South African cattle breeds