Adoption of the hyperbolic Cattaneo-Christov heatflow model in place of the more usual parabolic Fourier law is shown to raise the possibility of oscillatory convection in the classic Bénard problem of a Boussinesq fluid heated from below. By comparing the critical Rayleigh numbers for stationary and oscillatory convection, R c and R S respectively, oscillatory convection is found to represent the preferred form of instability whenever the Cattaneo number C exceeds a threshold value C T ≥ 8/27π 2 ≈ 0.03. In the case of free boundaries, analytical approaches permit direct treatment of the role played by the Prandtl number P 1 , which-in contrast to the classical stationary scenario-can impact on oscillatory modes significantly owing to the non-zero frequency of convection. Numerical investigation indicates that the behaviour found analytically for free boundaries applies in a qualitatively similar fashion for fixed boundaries, while the threshold Cattaneo number C T is computed as a function of P 1 ∈ [10 −2 , 10 +2 ] for both boundary regimes.

Recently, Early Warning Signals (EWS) have been developed to predict tipping points in Earth Systems. This discussion highlights the potential to apply EWS to human social and economic systems, which may also undergo similar critical transitions. Social tipping points are particularly difficult to predict, however, and the current formulation of EWS, based on a physical system analogy, may be insufficient. As an alternative set of EWS for social systems, we join with other authors encouraging a focus on heterogeneity, connectivity through social networks and individual thresholds to change.

Magnetic field generated by the Biermann battery is thought to be one of the principal mechanisms behind inhibition of heat-flow in laser-plasma interactions, and is predicted to grow exponentially in some contexts due to the thermomagnetic instability [Tidman & Shanny, Phys. Fluids 17 (1974)]. In contrast to these predictions, however, we have conducted Vlasov-Fokker-Planck simulations of magnetic field dynamics under a range of classically unstable laser-fusion conditions, and find field generation to be strongly suppressed, preventing magnetization of the transport, and stabilizing instability. By deriving new scaling laws, we show that this stabilization is a consequence of: (i) heavy suppression of the Biermann battery under non-local conditions; (ii) rapid convection of magnetic field by the heat-flow; and (iii) comparatively short field length-scales. Our results indicate that classical models substantially overestimate the importance of magnetic fields generated by the Biermann battery, and the susceptibility of laser-fusion plasmas to the thermomagnetic instability.

Inverse bremsstrahlung (IB) heating is known to distort the electron distribution function in laser-plasmas from a Gaussian towards a super-Gaussian, thereby modifying the equations of classical transport theory (Ridgers et al 2008 Phys. Plasmas 15 092311). Here we explore these modified equations, demonstrating that super-Gaussian effects both suppress traditional transport processes, while simultaneously introducing new effects, such as isothermal (anomalous Nernst) magnetic field advection up gradients in the electron number density n e , which we associate with a novel heat-flow q n ∝ ∇n e . Suppression of classical phenomena is shown to be most pronounced in the limit of low Hall-parameter χ, in which case the Nernst effect is reduced by a factor of five, the ∇T e × ∇n e field generation mechanism by ∼30% (where T e is the electron temperature), and the diffusive and Righi-Leduc heat-flows by ∼80 and ∼90% respectively. The new isothermal field advection phenomenon and associated density-gradient driven heat-flux q n are checked against kinetic simulation using the Vlasov-Fokker-Planck code impact, and interpreted in relation to the underlying super-Gaussian distribution through simplified kinetic