Local twistors and the conformal field equations

This note establishes the connection between Friedrich's conformal field equations and the conformally invariant formalism of local twistors.Comment: LaTeX2e Minor corrections of misprints et

Anti-self-dual conformal structures with null Killing vectors from projective structures

Using twistor methods, we explicitly construct all local forms of four--dimensional real analytic neutral signature anti--self--dual conformal structures $(M,[g])$ with a null conformal Killing vector. We show that $M$ is foliated by anti-self-dual null surfaces, and the two-dimensional leaf space inherits a natural projective structure. The twistor space of this projective structure is the quotient of the twistor space of $(M,[g])$ by the group action induced by the conformal Killing vector. We obtain a local classification which branches according to whether or not the conformal Killing vector is hyper-surface orthogonal in $(M, [g])$. We give examples of conformal classes which contain Ricci--flat metrics on compact complex surfaces and discuss other conformal classes with no Ricci--flat metrics.Comment: 43 pages, 4 figures. Theorem 2 has been improved: ASD metrics are given in terms of general projective structures without needing to choose special representatives of the projective connection. More examples (primary Kodaira surface, neutral Fefferman structure) have been included. Algebraic type of the Weyl tensor has been clarified. Final version, to appear in Commun Math Phy

Very Extended E8E_8 and A8A_8 at low levels, Gravity and Supergravity

We define a level for a large class of Lorentzian Kac-Moody algebras. Using this we find the representation content of very extended $A_{D-3}$ and $E_8$ (i.e. $E_{11}$) at low levels in terms of $A_{D-1}$ and $A_{10}$ representations respectively. The results are consistent with the conjectured very extended $A_8$ and $E_{11}$ symmetries of gravity and maximal supergravity theories given respectively in hep-th/0104081 and hep-th/0107209. We explain how these results provided further evidence for these conjectures.Comment: 16 pages, plain tex (equation 3.3 modified and one reference expanded

3-dimensional Cauchy-Riemann structures and 2nd order ordinary differential equations

The equivalence problem for second order ODEs given modulo point transformations is solved in full analogy with the equivalence problem of nondegenerate 3-dimensional CR structures. This approach enables an analog of the Feffereman metrics to be defined. The conformal class of these (split signature) metrics is well defined by each point equivalence class of second order ODEs. Its conformal curvature is interpreted in terms of the basic point invariants of the corresponding class of ODEs

Choosing Meteorological Input for the Global Modeling Initiative Assessment of High Speed Aircraft

The Global Modeling Initiative (GMI) science team is developing a three dimensional chemistry and transport model (CTM) to be used in assessment of the atmospheric effects of aviation. Requirements are that this model be documented, be validated against observations, use a realistic atmospheric circulation, and contain numerical transport and photochemical modules representing atmospheric processes. The model must also retain computational efficiency to be tractable to use for multiple scenarios and sensitivity studies. To meet these requirements, a facility model concept was developed in which the different components of the CTM are evaluated separately. The first use of the GMI model will be to evaluate the impact of the exhaust of supersonic aircraft on the stratosphere. The assessment calculations will depend strongly on the wind and temperature fields used by the CTM. Three meteorological data sets for the stratosphere are available to GMI: the National Center for Atmospheric Research Community Climate Model (CCM2), the Goddard Earth Observing System Data Assimilation System (GEOS DAS), and the Goddard Institute for Space Studies general circulation model (GISS). Objective criteria were established by the GMI team to identify the data set which provides the best representation of the stratosphere. Simulations of gases with simple chemical control were chosen to test various aspects of model transport. The three meteorological data sets were evaluated and graded based on their ability to simulate these aspects of stratospheric measurements. This paper describes the criteria used in grading the meteorological fields. The meteorological data set which has the highest score and therefore was selected for GMI is CCM2. This type of objective model evaluation establishes a physical basis for interpretation of differences between models and observations. Further, the method provides a quantitative basis for defining model errors, for discriminating between different models, and for ready re-evaluation of improved models. These in turn will lead to a higher level of confidence in assessment calculations

Application of Discrete Differential Forms to Spherically Symmetric Systems in General Relativity

In this article we describe applications of Discrete Differential Forms in computational GR. In particular we consider the initial value problem in vacuum space-times that are spherically symmetric. The motivation to investigate this method is mainly its manifest coordinate independence. Three numerical schemes are introduced, the results of which are compared with the corresponding analytic solutions. The error of two schemes converges quadratically to zero. For one scheme the errors depend strongly on the initial data.Comment: 22 pages, 6 figures, accepted by Class. Quant. Gra

Currents and Superpotentials in classical gauge invariant theories I. Local results with applications to Perfect Fluids and General Relativity

E. Noether's general analysis of conservation laws has to be completed in a Lagrangian theory with local gauge invariance. Bulk charges are replaced by fluxes of superpotentials. Gauge invariant bulk charges may subsist when distinguished one-dimensional subgroups are present. As a first illustration we propose a new {\it Affine action} that reduces to General Relativity upon gauge fixing the dilatation (Weyl 1918 like) part of the connection and elimination of auxiliary fields. It allows a comparison of most gravity superpotentials and we discuss their selection by the choice of boundary conditions. A second and independent application is a geometrical reinterpretation of the convection of vorticity in barotropic nonviscous fluids. We identify the one-dimensional subgroups responsible for the bulk charges and thus propose an impulsive forcing for creating or destroying selectively helicity. This is an example of a new and general Forcing Rule.Comment: 64 pages, LaTeX. Version 2 has two more references and one misprint corrected. Accepted in Classical and Quantum Gravit

Point Mutations in HpuB Enable Gonococcal HpuA Deletion Mutants To Grow on Hemoglobin

Neisseria gonorrhoeae ordinarily requires both HpuA and HpuB to use hemoglobin (Hb) as a source of iron for growth. Deletion of HpuA resulted in reduced Hb binding and failure of growth on Hb. We identified rare Hb-utilizing colonies (Hb+) from an hpuA deletion mutant of FA1090, which fell into two phenotypic classes. One class of the Hb+ revertants required expression of both TonB and HpuB for growth on Hb, while the other class required neither TonB nor HpuB. All TonB/HpuB-dependent mutants had single amino acid alterations in HpuB, which occurred in clusters, particularly near the C terminus. The point mutations in HpuB did not restore normal Hb binding. Human serum albumin inhibited Hb-dependent growth of HpuB point mutants lacking HpuA but did not inhibit growth when expression of HpuA was restored. Thus, HpuB point mutants internalized heme in the absence of HpuA despite reduced binding of Hb. HpuA facilitated Hb binding and was important in allowing use of heme from Hb for growth

Gonococci with mutations to low-level penicillin resistance exhibit increased sensitivity to the oxygen-independent bactericidal activity of human polymorphonuclear leukocyte granule extracts.

Gonococci which cause disseminated gonococcal infection are nearly always highly penicillin sensitive, in contrast to many isolates causing uncomplicated gonorrhea. We questioned whether any of the known chromosomal mutations to low-level penicillin resistance might adversely affect virulence. The penA2 locus is known to result in low-level resistance to penicillins, whereas mtr-2 results in nonspecific resistance to a variety of antimicrobial agents. We found that the penA2 and mtr-2 mutations each markedly increased sensitivity of strain FA19 to oxygen-independent killing by human polymorphonuclear leukocyte mixed or isolated azurophilic granule extracts. The penA2 and mtr-2 mutations had no effect on sensitivity to serum antibody and complement. Isogenic opaque or transparent variants of several strains of Neisseria gonorrhoeae were equally resistant to human polymorphonuclear leukocyte mixed granule extract bactericidal systems. There were also no differences in susceptibility of piliated type 1 and nonpiliated type 4 variants to human polymorphonuclear leukocyte mixed granule extracts. Since the penA2 and mtr-2 loci are known to increase the degree of cross-linking of cell wall peptidoglycan, the structure of peptidoglycan apparently affects sensitivity to killing by one or more polymorphonuclear leukocyte azurophilic granule extract bactericidal systems. These observations might explain why gonococci with mutations similar to penA2 and mtr-2 are almost never isolated from patients with disseminated gonococcal infection

Covariance properties and regularization of conserved currents in tetrad gravity

We discuss the properties of the gravitational energy-momentum 3-form within the tetrad formulation of general relativity theory. We derive the covariance properties of the quantities describing the energy-momentum content under Lorentz transformations of the tetrad. As an application, we consider the computation of the total energy (mass) of some exact solutions of Einstein's general relativity theory which describe compact sources with asymptotically flat spacetime geometry. As it is known, depending on the choice of tetrad frame, the formal total integral for such configurations may diverge. We propose a natural regularization method which yields finite values for the total energy-momentum of the system and demonstrate how it works on a number of explicit examples.Comment: 36 pages, Revtex, no figures; small changes, published versio