Study of transport coefficients in ultrarelativistic kinetic theory

A spatially-periodic longitudinal wave is considered in relativistic dissipative hydrodynamics. At sufficiently small wave amplitudes, an analytic solution is obtained in the linearised limit of the macroscopic conservation equations within the first- and second-order relativistic hydrodynamics formulations. A kinetic solver is used to obtain the numerical solution of the relativistic Boltzmann equation for massless particles in the Anderson-Witting approximation for the collision term. It is found that, at small values of the Anderson-Witting relaxation time $\tau$, the transport coefficients emerging from the relativistic Boltzmann equation agree with those predicted through the Chapman-Enskog procedure, while the relaxation times of the heat flux and shear pressure are equal to $\tau$. These claims are further strengthened by considering a moment-type approximation based on orthogonal polynomials under which the Chapman-Enskog results for the transport coefficients are exactly recovered.Comment: 34 pages (double column), 15 figures. Version accepted for publication in PR

Quantum non-equilibrium effects in rigidly-rotating thermal states

Based on known analytic results, the thermal expectation value of the stress-energy tensor (SET) operator for the massless Dirac field is analyzed from a hydrodynamic perspective. Key to this analysis is the Landau decomposition of the SET, with the aid of which we find terms which are not present in the ideal SET predicted by kinetic theory. Moreover, the quantum corrections become dominant in the vicinity of the speed of light surface (SOL). While rigidly-rotating thermal states cannot be constructed for the Klein-Gordon field, we perform a similar analysis at the level of quantum corrections previously reported in the literature and we show that the Landau frame is well-defined only when the system is enclosed inside a boundary located inside or on the SOL. We discuss the relevance of these results for accretion disks around rapidly-rotating pulsars.Comment: 6 pages, 2 figures, accepted for publication in Physics Letters

Secular trends and latitude gradients in sex ratios at birth in Australia and New Zealand (1950- 2010) demonstrate uncharacteristic homogeneity

Introduction: The male to female ratio of live births is expressed as the ratio of male live births divided by total live births (M/F). Although this would be more accurately abbreviated as M/T (male births divided by total births), it is widely (albeit technically incorrectly) abbreviated as M/F, and this will be used throughout. Globally, over the past four decades, this is expected to be 0.515, with a slight (1.5%) male excess. M/F exhibits an unexplained contrasting latitude gradient. More males are born towards the south of Europe, and the south of Asia, while more males are born toward the north in North American continent. M/F is also declining overall, in both of these continents. This study investigates secular trends and latitude gradients in M/F in Australia and New Zealand from a World Health Organization (WHO) dataset that includes the past sixty years. Methods: Permission was obtained to source WHO datasets going back to 1950, following which Microsoft Excel was used to calculate M/F ratios. Australian and New Zealand data were available for the years 1950-2006 and 1950-2009 respectively. Chi tests for trend were used for annual male and female births. These were performed using the Bio-Med-Stat Excel add-in for contingency tables. Results: There were 17035325 births for Australia and New Zealand during this period. M/F ratios ranged between 0.507-0.519. No latitude variations in M/F were found between Australia (9° to 44°) and New Zealand (29° to 53°). The overall M/F was 0.5134 - lower than the anticipated 0.515, with an estimated male birth deficit of 28009. Cycles of 30 years duration are apparent in the dataset but not at statistically significant levels. Discussion: The lack of latitude gradient in this region is not unexpected as there is a wide latitude overlap between Australia and New Zealand. It has been hypothesised that M/F exhibits a 30 year cycle due to an unknown mechanism that negatively correlates M/F with the adult sex ratio at the time of conception. Conclusion: The factor/s that are causing a decline in M/F ratios in Europe, North America and Asia are absent or not so strongly influential in Australasia.peer-reviewe

Anderson-Witting transport coefficients for flows in general relativity

The transport coefficients induced by the Anderson-Witting approximation of the collision term in the relativistic Boltzmann equation are derived for close to equilibrium flows in general relativity. Using the tetrad formalism, it is shown that the expression for these coefficients is the same as that obtained on flat space-time, in agreement with the generalized equivalence principle.Comment: 6 pages, 1 figure, proceedings of TIM 15-16 conference (26-28 May 2016, Timisoara, Romania