The Conformal Einstein Field Equations with Massless Vlasov Matter

We prove the stability of de Sitter space-time as a solution to the Einstein-Vlasov system with massless particles. The semi-global stability of Minkowski space-time is also addressed. The proof relies on conformal techniques, namely Friedrich's conformal Einstein field equations. We exploit the conformal invariance of the massless Vlasov equation on the cotangent bundle and adapt Kato's local existence theorem for symmetric hyperbolic systems to prove a long enough time of existence for solutions of the evolution system implied by the Vlasov equation and the conformal Einstein field equations.Comment: 27 pages. To appear in Ann. Inst. Fourie

Performance Mapping Studies in Redox Flow Cells

Pumping power requirements in any flow battery system constitute a direct parasitic energy loss. It is therefore useful to determine the practical lower limit for reactant flow rates. Through the use of a theoretical framework based on electrochemical first principles, two different experimental flow mapping techniques were developed to evaluate and compare electrodes as a function of flow rate. For the carbon felt electrodes presently used in NASA-Lewis Redox cells, a flow rate 1.5 times greater than the stoichiometric rate seems to be the required minimum

Zero-energy states and fragmentation of spin in the easy-plane antiferromagnet on a honeycomb lattice

The core of the vortex in the Neel order parameter for an easy-plane antiferromagnet on honeycomb lattice is demonstrated to bind two zero-energy states. Remarkably, a single electron occupying this mid-gap band has its spin fragmented between the two sublattices: Whereas it yields a vanishing total magnetization it shows a finite Neel order, orthogonal to the one of the assumed background. The requisite easy-plane anisotropy may be introduced by a magnetic field parallel to the graphene layer, for example. The results are relevant for spin-1/2 fermions on graphene's or optical honeycomb lattice, in the strongly interacting regime.Comment: 4 pages; cosmetic changes; published versio

NASA Redox cell stack shunt current, pumping power, and cell performance tradeoffs

The NASA Redox energy storage system is under active technology development. The hardware undergoing laboratory testing is either 310 sq. cm. or 929 sq. cm. (0.33 sq. ft. or 1.0 sq. ft. per cell active area with up to 40 individual cells connected to make up a modular cell stack. This size of hardware allows rather accurate projections to be made of the shunt power/pump power tradeoffs. The modeling studies that were completed on the system concept are reviewed along with the approach of mapping the performance of Redox cells over a wide range of flow rates and depths of discharge of the Redox solutions. Methods are outlined for estimating the pumping and shunt current losses for any type of cell and stack combination. These methods are applicable to a variety of pumping options that are present with Redox systems. The results show that a fully developed Redox system has acceptable parasitic losses when using a fixed flow rate adequate to meet the worst conditions of current density and depth of discharge. These losses are reduced by about 65 percent if variable flow schedules are used. The exact value of the overall parasitics will depend on the specific system requirements of current density, voltage limits, charge, discharge time, etc

Design principles for nickel-hydrogen cells and batteries

Nickel-hydrogen cells and, more recently, bipolar batteries have been built by a variety of organizations. The design principles that have been used by the technology group at the NASA Lewis Research Center draw upon their extensive background in separator technology, alkaline fuel cell technology, and several alkaline cell technology areas. These design principles have been incorporated into both the more contemporary individual pressure vessel (IPV) designs that were pioneered by other groups, as well as the more recent bipolar battery designs using active cooling that are being developed at NASA Lewis Research Center and under contract. These principles are rather straightforward applications of capillary force formalisms, coupled with the slowly developing data base resulting from careful post test analyses. The objective of this overall effort is directed towards the low-Earth-orbit (LEO) application where the cycle life requirements are much more severe than the geosynchronous-orbit (GEO) application. A summary of the design principles employed is presented along with a discussion of the recommendations for component pore sizes and pore size distributions, as well as suggested materials of construction. These will be made based on our experience in these areas to show how these design principles have been translated into operating hardware

Trapped ion emulation of electric dipole moment of neutral relativistic particles

The electric dipole moments of various neutral elementary particles, such as neutron, neutrinos, certain hypothetical dark matter particles and others, are predicted to exist by the standard model of high energy physics and various extensions of it. However, the predicted values are beyond the present experimental capabilities. We propose to simulate and emulate the electric dipole moment of neutral relativistic particles and the ensuing effects in the presence of electrostatic field by emulation of an extended Dirac equation in ion traps

States of the Dirac equation in confining potentials

We study the Dirac equation in confining potentials with pure vector coupling, proving the existence of metastable states with longer and longer lifetimes as the non-relativistic limit is approached and eventually merging with continuity into the Schr\"odinger bound states. We believe that the existence of these states could be relevant in high energy model construction and in understanding possible resonant scattering effects in systems like Graphene. We present numerical results for the linear and the harmonic cases and we show that the the density of the states of the continuous spectrum is well described by a sum of Breit-Wigner lines. The width of the line with lowest positive energy, as expected, reproduces very well the Schwinger pair production rate for a linear potential: we thus suggest a different way of obtaining informations on the pair production in unbounded, non uniform electric fields, where very little is known.Comment: 4 page

Symmetry Breaking of Relativistic Multiconfiguration Methods in the Nonrelativistic Limit

The multiconfiguration Dirac-Fock method allows to calculate the state of relativistic electrons in atoms or molecules. This method has been known for a long time to provide certain wrong predictions in the nonrelativistic limit. We study in full mathematical details the nonlinear model obtained in the nonrelativistic limit for Be-like atoms. We show that the method with sp+pd configurations in the J=1 sector leads to a symmetry breaking phenomenon in the sense that the ground state is never an eigenvector of L^2 or S^2. We thereby complement and clarify some previous studies.Comment: Final version, to appear in Nonlinearity. Nonlinearity (2010) in pres

Zitterbewegung of relativistic electrons in a magnetic field and its simulation by trapped ions

One-electron 3+1 and 2+1 Dirac equations are used to calculate the motion of a relativistic electron in a vacuum in the presence of an external magnetic field. First, calculations are carried on an operator level and exact analytical results are obtained for the electron trajectories which contain both intraband frequency components, identified as the cyclotron motion, as well as interband frequency components, identified as the trembling motion (Zitterbewegung, ZB). Next, time-dependent Heisenberg operators are used for the same problem to compute average values of electron position and velocity employing Gaussian wave packets. It is shown that the presence of a magnetic field and the resulting quantization of the energy spectrum has pronounced effects on the electron Zitterbewegung: it introduces intraband frequency components into the motion, influences all the frequencies and makes the motion stationary (not decaying in time) in case of the 2+1 Dirac equation. Finally, simulations of the 2+1 Dirac equation and the resulting electron ZB in the presence of a magnetic field are proposed and described employing trapped ions and laser excitations. Using simulation parameters achieved in recent experiments of Gerritsma and coworkers we show that the effects of the simulated magnetic field on ZB are considerable and can certainly be observed.Comment: 19 pages, 9 figures, published versio

The Dirac equation without spinors

In the first part of the paper we give a tensor version of the Dirac equation. In the second part we formulate and analyse a simple model equation which for weak external fields appears to have properties similar to those of the 2--dimensional Dirac equation.Comment: 20 pages. Submitted for publication in the proceedings of the conference `Functional analysis, partial differential equations and applications', Rostock (Germany) 31 August--4 September 199