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

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 #

Fundamental Limits to Position Determination by Concentration Gradients

Position determination in biological systems is often achieved through protein concentration gradients. Measuring the local concentration of such a protein with a spatially-varying distribution allows the measurement of position within the system. In order for these systems to work effectively, position determination must be robust to noise. Here, we calculate fundamental limits to the precision of position determination by concentration gradients due to unavoidable biochemical noise perturbing the gradients. We focus on gradient proteins with first order reaction kinetics. Systems of this type have been experimentally characterised in both developmental and cell biology settings. For a single gradient we show that, through time-averaging, great precision can potentially be achieved even with very low protein copy numbers. As a second example, we investigate the ability of a system with oppositely directed gradients to find its centre. With this mechanism, positional precision close to the centre improves more slowly with increasing averaging time, and so longer averaging times or higher copy numbers are required for high precision. For both single and double gradients, we demonstrate the existence of optimal length scales for the gradients, where precision is maximized, as well as analyzing how precision depends on the size of the concentration measuring apparatus. Our results provide fundamental constraints on the positional precision supplied by concentration gradients in various contexts, including both in developmental biology and also within a single cell.Comment: 24 pages, 2 figure

Long distance contribution to B−→K−K−π+B^- \to K^- K^- \pi^+, - a searching ground mode for new physics

The decay $B^- \to K^- K^- \pi^+$ has been sugested as a test for minimal supersymmetric standard model and for supersymmetric models with R-parity violating couplings, in view of its extreme smallnesss in the standard model. We calculate two long distance contributions to this decay, that associated with $DD$ and $D\pi$ intermediate states and that induced by virtual $D$, $\pi$ mesons. The branching ratio due to these contributions is $6 \times 10^{-12}$, which is somewhat smaller than the standard model short distance result, leaving this decay free for the search of new physics.Comment: 13 pages, 2 figures, revised versio

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

The externides of Wopmay Orogen, Point Lake and Kikerk Lake map areas, District of Mackenzie

Some results of recent field work are briefly discussed as they pertain to the following topics: (1) north-south stratigraphic continuity of the Precambrian continental-terrace wedge, (2) stromatolite elongation, paleowind direction and global polarity during deposition of the Rocknest dolomite shelf, (3) evidence for primary aragonitic mineralogy of the Rocknest Formation, (4) attempted quantitative paleobathymetry of the upper continental slope, (5) eastward migration of foredeep flysch, (6) nature of basement involvement in Asiak Fold-Thrust Belt, (7) relation of thrusting to the foredeep molasse, (8) mysterious basement-involved cross folding of regional extent, (9) normal faults associated with late transcurrent faulting , and (10) the first reported minor leadzinc vein mineralization in Rocknest dolomite. Future field work is outlined

Existence of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system

Using ODE techniques we prove the existence of large classes of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system. These include data for which the ratio of total charge to total mass is arbitrarily large.Comment: 12 page

Structural response of a steel-frame building to horizontal and vertical travelling fires in multiple floors

During previous fire events such as the World Trade Centre Towers (WTC) 1, 2 & 7 in New York (2001), the Windsor Tower in Madrid (2005), and the Plasco building in Iran (2017), flames were observed to travel horizontally across the floor plate and vertically to different floors. Such fires are not considered as part of the traditional prescriptive structural design for fire. Recently, the Travelling Fires Methodology (TFM) has been developed to account for such horizontally travelling nature of fires. A dozen of studies have investigated the structural response of steel, concrete, and composite structures to a single-floor travelling fire. 5 out of 6 of the vertically travelling fire studies have been limited to the structures with a long span composite truss system as in the WTC Towers. The aim of this work is to investigate the response of a substantially different structural system, i.e. a generic multi-storey steel frame, subjected to travelling fires in multiple floors, and varying the number of fire floors, including horizontal and vertical fire spread. A two-dimensional 10-storey 5-bay steel frame is modelled in the finite element software LS-DYNA. The number of multiple fire floors is varied between 1 and 10, and for each of these scenarios, 5 different fire types are investigated. They include four travelling fire scenarios and the standard fire. In total, 51 fire simulations are considered. The development of deflections, axial forces, bending moments and frame utilization are analysed. Results show that the largest stresses develop in the fire floors adjacent to cool floors, and their behaviour is independent of the number of fire floors. Results indicate that both the fire type and the number of fire floors have a significant effect on the failure time (i.e. exceeded element load carrying capacity) and the type of collapse mechanism. In the cases with a low number of fire floors (1–3) failure is dominated by the loss of material strength, while in the cases with larger number of fire floors (5–10) failure is dominated by thermal expansion. Collapse is mainly initiated by the pull-in of external columns (1–3-floor fires; 1–9-floor fires for 2.5% TFM) or swaying of the frame to the side of fire origin (5–10-floor fires). This study has assessed a different structural form compared to previous literature under an extensive range of multiple floor travelling fire scenarios. We find that although vertically travelling fires result in larger beam axial forces and initial deflections, simultaneous travelling fires result in shorter failure times and represent a more onerous scenario for the steel frame investigated

Flat galaxies with dark matter halos - existence and stability

We consider a model for a flat, disk-like galaxy surrounded by a halo of dark matter, namely a Vlasov-Poisson type system with two particle species, the stars which are restricted to the galactic plane and the dark matter particles. These constituents interact only through the gravitational potential which stars and dark matter create collectively. Using a variational approach we prove the existence of steady state solutions and their nonlinear stability under suitably restricted perturbations.Comment: 39 page