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

Desorption of Ammonium from Montmorillonite Clay

The clay minerals are extremely important constituents of the inorganic solid phase of the soil primarily because of their ability to adsorb cations. Some clay minerals are capable of adsorbing certain cations so tenaciously, that these ions cannot be readily extracted with a neutral solution of a salt. Potassium and ammonium are nutrient cations that may suffer a decrease in their availability to plants by this phenomenon, which is commonly referred to as cation fixation. This research was undertaken to study the behavior of ammonium ions adsorbed by montmorillonite as affected by heating at various temperatures and to test the hypothesis that ammonium ions are adsorbed with varying levels of energy, depending on the site of adsorption. It is postulated that the fixation of cations is dependent upon the site of adsorption alone, and that fixed cations can be identified by the significantly greater demand for the energy required for desorption of such ions

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

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 #

Higher Twist, ξw\xi_w Scaling, and Effective LOPDFsLO PDFs for Lepton Scattering in the Few GeV Region

We use a new scaling variable $\xi_w$, and add low $Q^2$ modifications to GRV98 leading order parton distribution functions such that they can be used to model electron, muon and neutrino inelastic scattering cross sections (and also photoproduction) at both very low and high energies.Comment: 6 pages, 3 figures. To be published in J. Phys. G (Conf. Proceedings) based on two talks by Arie Bodek at the NuFact$'02$ conference, Imperial College, London, England, July 200