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

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

Critical collapse of collisionless matter - a numerical investigation

In recent years the threshold of black hole formation in spherically symmetric gravitational collapse has been studied for a variety of matter models. In this paper the corresponding issue is investigated for a matter model significantly different from those considered so far in this context. We study the transition from dispersion to black hole formation in the collapse of collisionless matter when the initial data is scaled. This is done by means of a numerical code similar to those commonly used in plasma physics. The result is that for the initial data for which the solutions were computed, most of the matter falls into the black hole whenever a black hole is formed. This results in a discontinuity in the mass of the black hole at the onset of black hole formation.Comment: 22 pages, LaTeX, 7 figures (ps-files, automatically included using psfig

Scaling-up experiments of smouldering combustion as a remediation technology for contaminated soil

Self-sustaining Treatment for Active Remediation (STAR) is a novel, patent-pending process that uses smouldering combustion as a remediation technology for land contaminated with hazardous organic liquids. Compounds such as chlorinated solvents, coal tar and petroleum products, called Non-Aqueous Phase Liquids (NAPLs) for their low miscibility with water, have a long history of use in the industrialised world and are among the most ubiquitous of contaminants worldwide. These contaminants are toxic and many are suspected or known carcinogens. Existing remediation technologies are expensive and ineffective at reducing NAPL source zones sufficiently to restore affected water resources to appropriate quality levels. STAR introduces a self-sustaining smouldering reaction within the NAPL pool in the subsurface and allows that reaction to provide all of the post-ignition energy required by the reaction to completely remediate the NAPL source zone in the soil. Results from laboratory and field experiments have been very promising. Laboratory experiments have demonstrated STAR across a wide range of NAPL fuels and focused on coal tar to identify key parameters for successful remediation. Modelling has suggested that STAR efficiency will improve with scale as effects such as heat losses from boundaries become less significant. Observations from field experiments support the modelling theory - significantly lower relative air flow in a smouldering field experiment (330L) led to faster smouldering front propagation than observed in laboratory experiments (1L and 3L). Preliminary emissions monitoring by Fourier Transform Infrared (FTIR) spectroscopy has suggested that STAR emissions might be low enough to meet regulatory requirements, but further study is necessary. As emissions are expected to vary with each contaminant, activated carbon filters are being developed and tested in case emissions filtration is necessary. Experiments at all scales have demonstrated that STAR is controllable and self-terminating. Pilot-scale (2500L) field trials are underway to demonstrate STAR on excavated contaminated soil. The materials that will be studied in these trials are manufactured coal tar in coarse sand (which is the same material as used in the laboratory and field experiments) as well as two soils obtained from coal tar contaminated sites. This poster focuses on the scale-up to these field trials, including small scale characterisation, large scale performance, emissions monitoring and post-treatment soil analysis

Experimental studies of self-sustaining thermal aquifer remediation (STAR) for non-aqueous phase liquid (NAPL) sources

Self-sustaining Thermal Aquifer Remediation (STAR) is a novel technology that employs smouldering combustion for the remediation of subsurface contamination by non-aqueous phase liquids (NAPLs). Smouldering is a form of combustion that is slower and less energetic than flaming combustion. Familiar examples of smouldering involve solid fuels that are destroyed by the reaction (e.g., a smouldering cigarette or peat smouldering after a wildfire). In STAR, the NAPL serves as the fuel within an inert, porous soil medium. Results from experiments across a range of scales are very promising. Detailed characterisation has focused on coal tar, a common denser-than-water NAPL (DNAPL) contaminant. Complete remediation is demonstrated across this range of scales. Visual observations are supported bychemical extraction results. Further experiments suggest that STAR can be self-sustaining, meaning that once ignited the process can supply its own energy to propagate. Costly energy input is reduced significantly. Comparison of large scale to small scale laboratory experiments, a volume increase by a factor of 100, suggests that STAR process efficiency increases with scale. This increase in efficiency results from reduced heat losses at larger scales while maximum the temperature achieved by STAR is unaffected. The research also demonstrates the controllability of STAR, where the termination of airflow to the reaction terminates the STAR process. The scale-up process provides important guidance to the development of full scale STAR for ex situ remediation of NAPL-contaminated soil

Global existence of classical solutions to the Vlasov-Poisson system in a three dimensional, cosmological setting

The initial value problem for the Vlasov-Poisson system is by now well understood in the case of an isolated system where, by definition, the distribution function of the particles as well as the gravitational potential vanish at spatial infinity. Here we start with homogeneous solutions, which have a spatially constant, non-zero mass density and which describe the mass distribution in a Newtonian model of the universe. These homogeneous states can be constructed explicitly, and we consider deviations from such homogeneous states, which then satisfy a modified version of the Vlasov-Poisson system. We prove global existence and uniqueness of classical solutions to the corresponding initial value problem for initial data which represent spatially periodic deviations from homogeneous states.Comment: 23 pages, Latex, report #

Spherically symmetric steady states of galactic dynamics in scalar gravity

The kinetic motion of the stars of a galaxy is considered within the framework of a relativistic scalar theory of gravitation. This model, even though unphysical, may represent a good laboratory where to study in a rigorous, mathematical way those problems, like the influence of the gravitational radiation on the dynamics, which are still beyond our present understanding of the physical model represented by the Einstein--Vlasov system. The present paper is devoted to derive the equations of the model and to prove the existence of spherically symmetric equilibria with finite radius.Comment: 13 pages, mistypos correcte

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

Small-scale forward smouldering experiments for remediation of coal tar in inert media

This paper presents a series of experiments conducted to assess the potential of smouldering combustion as a novel technology for remediation of contaminated land by water-immiscible organic compounds. The results from a detailed study of the conditions under which a smouldering reaction propagates in sand embedded with coal tar are presented. The objective of the study is to provide further understanding of the governing mechanisms of smouldering combustion of liquids in porous media. A small-scale apparatus consisting of a 100 mm in diameter quartz cylinder arranged in an upward configuration was used for the experiments. Thermocouple measurements and visible digital imaging served to track and characterize the ignition and propagation of the smouldering reaction. These two diagnostics are combined here to provide valuable information on the development of the reaction front. Post-treatment analyses of the sand were used to assess the amount of coal tar remaining in the soil. Experiments explored a range of inlet airflows and fuel concentrations. The smouldering ignition of coal tar was achieved for all the conditions presented here and self-sustained propagation was established after the igniter was turned off. It was found that the combustion is oxygen limited and peak temperatures in the range 800-1080 °C were observed. The peak temperature increased with the airflow at the lower range of flows but decreased with airflow at the higher range of flows. Higher airflows were found to produce faster propagation. Higher fuel concentrations were found to produce higher peak temperatures and slower propagation. The measured mass removal of coal tar was above 99% for sand obtained from the core and 98% for sand in the periphery of the apparatus