Spherically symmetric equilibria for self-gravitating kinetic or fluid models in the non-relativistic and relativistic case - A simple proof for finite extension

We consider a self-gravitating collisionless gas as described by the Vlasov-Poisson or Einstein-Vlasov system or a self-gravitating fluid ball as described by the Euler-Poisson or Einstein-Euler system. We give a simple proof for the finite extension of spherically symmetric equilibria, which covers all these models simultaneously. In the Vlasov case the equilibria are characterized by a local growth condition on the microscopic equation of state, i.e., on the dependence of the particle distribution on the particle energy, at the cut-off energy E_0, and in the Euler case by the corresponding growth condition on the equation of state p=P(\rho) at \rho=0. These purely local conditions are slight generalizations to known such conditions.Comment: 20 page

Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system

We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the formation of a trapped surface in the evolution which in particular implies that weak cosmic censorship holds for these data. We also analyze the evolution of solutions after a trapped surface has formed and we show that the event horizon is future complete. Furthermore we find that the apparent horizon and the event horizon do not coincide. This behavior is analogous to what is found in certain Vaidya spacetimes. The analysis is carried out in Eddington-Finkelstein coordinates.Comment: 2

Thermochemical Conversion of Biomass in Smouldering Combustion across Scales: the Roles of Heterogeneous Kinetics, Oxygen and Transport Phenomena

AbstractThe thermochemical conversion of biomass in smouldering combustion is investigated here by combining experiments and modeling at two scales: matter (1mg) and bench (100g) scales. Emphasis is put on the effect of oxygen (0–33vol.%) and oxidation reactions because these are poorly studied in the literature in comparison to pyrolysis. The results are obtained for peat as a representative biomass for which there is high-quality experimental data published previously. Three kinetic schemes are explored, including various steps of drying, pyrolysis and oxidation. The kinetic parameters are found using the Kissinger–Genetic Algorithm method, and then implemented in a one-dimensional model of heat and mass transfer. The predictions are validated with thermogravimetric and bench-scale experiments and then analyzed to unravel the role of heterogeneous reaction. This is the first time that the influence of oxygen on biomass smouldering is explained in terms of both chemistry and transport phenomena across scales

Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter

We prove a new global existence result for the asymptotically flat, spherically symmetric Einstein-Vlasov system which describes in the framework of general relativity an ensemble of particles which interact by gravity. The data are such that initially all the particles are moving radially outward and that this property can be bootstrapped. The resulting non-vacuum spacetime is future geodesically complete.Comment: 16 page

Existence of axially symmetric static solutions of the Einstein-Vlasov system

We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the implicit function theorem by perturbing off a suitable spherically symmetric steady state of the Vlasov-Poisson system.Comment: 32 page

On the Einstein-Vlasov system with hyperbolic symmetry

It is shown that a spacetime with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry can be globally covered by compact hypersurfaces on which the mean curvature is constant and by compact hypersurfaces on which the area radius is constant. Results for the related cases of spherical and plane symmetry are reviewed and extended. The prospects of using the global time coordinates obtained in this way to investigate the global geometry of the spacetimes concerned are discusse

On the steady states of the spherically symmetric Einstein-Vlasov system

Using both numerical and analytical tools we study various features of static, spherically symmetric solutions of the Einstein-Vlasov system. In particular, we investigate the possible shapes of their mass-energy density and find that they can be multi-peaked, we give numerical evidence and a partial proof for the conjecture that the Buchdahl inequality $\sup_{r > 0} 2 m(r)/r < 8/9$, $m(r)$ the quasi-local mass, holds for all such steady states--both isotropic {\em and} anisotropic--, and we give numerical evidence and a partial proof for the conjecture that for any given microscopic equation of state--both isotropic {\em and} anisotropic--the resulting one-parameter family of static solutions generates a spiral in the radius-mass diagram.Comment: 34 pages, 18 figures, LaTe

A non-variational approach to nonlinear stability in stellar dynamics applied to the King model

In previous work by Y. Guo and G. Rein, nonlinear stability of equilibria in stellar dynamics, i.e., of steady states of the Vlasov-Poisson system, was accessed by variational techniques. Here we propose a different, non-variational technique and use it to prove nonlinear stability of the King model against a class of spherically symmetric, dynamically accessible perturbations. This model is very important in astrophysics and was out of reach of the previous techniques

Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant

The behaviour of expanding cosmological models with collisionless matter and a positive cosmological constant is analysed. It is shown that under the assumption of plane or hyperbolic symmetry the area radius goes to infinity, the spacetimes are future geodesically complete, and the expansion becomes isotropic and exponential at late times. This proves a form of the cosmic no hair theorem in this class of spacetimes

Experimental study of the formation and collapse of an overhang in the lateral spread of smouldering peat fires

Smouldering combustion is the driving phenomenon of wildfires in peatlands, and is responsible for large amounts of carbon emissions and haze episodes world wide. Compared to flaming fires, smouldering is slow, low-temperature, flameless, and most persistent, yet it is poorly understood. Peat, as a typical organic soil, is a porous and charring natural fuel, thus prone to smouldering. The spread of smouldering peat fire is a multidimensional phenomenon, including two main components: in-depth vertical and surface lateral spread. In this study, we investigate the lateral spread of peat fire under various moisture and wind conditions. Visual and infrared cameras as well as a thermocouple array are used to measure the temperature profile and the spread rate. For the first time the overhang, where smouldering spreads fastest beneath the free surface, is observed in the laboratory, which helps understand the interaction between oxygen supply and heat losses. The periodic formation and collapse of overhangs is observed. The overhang thickness is found to increase with moisture and wind speed, while the spread rate decreases with moisture and increases with wind speed. A simple theoretical analysis is proposed and shows that the formation of overhang is caused by the spread rate difference between the top and lower peat layers as well as the competition between oxygen supply and heat losses