Turbulence and turbulent mixing in natural fluids

Turbulence and turbulent mixing in natural fluids begins with big bang turbulence powered by spinning combustible combinations of Planck particles and Planck antiparticles. Particle prograde accretions on a spinning pair releases 42% of the particle rest mass energy to produce more fuel for turbulent combustion. Negative viscous stresses and negative turbulence stresses work against gravity, extracting mass-energy and space-time from the vacuum. Turbulence mixes cooling temperatures until strong-force viscous stresses freeze out turbulent mixing patterns as the first fossil turbulence. Cosmic microwave background temperature anisotropies show big bang turbulence fossils along with fossils of weak plasma turbulence triggered as plasma photon-viscous forces permit gravitational fragmentation on supercluster to galaxy mass scales. Turbulent morphologies and viscous-turbulent lengths appear as linear gas-proto-galaxy-clusters in the Hubble ultra-deep-field at z~7. Proto-galaxies fragment into Jeans-mass-clumps of primordial-gas-planets at decoupling: the dark matter of galaxies. Shortly after the plasma to gas transition, planet-mergers produce stars that explode on overfeeding to fertilize and distribute the first life.Comment: 23 pages 12 figures, Turbulent Mixing and Beyond 2009 International Center for Theoretical Physics conference, Trieste, Italy. Revision according to Referee comments. Accepted for Physica Scripta Topical Issue to be published in 201

Hamiltonian Formulation of Two Body Problem in Wheeler-Feynman electrodynamics

A Hamiltonian formulation for the classical problem of electromagnetic interaction of two charged relativistic particles is found.Comment: 22 pages, 8 Uuencoded Postscript figure

Global embedding of the Kerr black hole event horizon into hyperbolic 3-space

An explicit global and unique isometric embedding into hyperbolic 3-space, H^3, of an axi-symmetric 2-surface with Gaussian curvature bounded below is given. In particular, this allows the embedding into H^3 of surfaces of revolution having negative, but finite, Gaussian curvature at smooth fixed points of the U(1) isometry. As an example, we exhibit the global embedding of the Kerr-Newman event horizon into H^3, for arbitrary values of the angular momentum. For this example, considering a quotient of H^3 by the Picard group, we show that the hyperbolic embedding fits in a fundamental domain of the group up to a slightly larger value of the angular momentum than the limit for which a global embedding into Euclidean 3-space is possible. An embedding of the double-Kerr event horizon is also presented, as an example of an embedding which cannot be made global.Comment: 16 pages, 13 figure

The Relation between Physical and Gravitational Geometry

The appearance of two geometries in one and the same gravitational theory is familiar. Usually, as in the Brans-Dicke theory or in string theory, these are conformally related Riemannian geometries. Is this the most general relation between the two geometries allowed by physics ? We study this question by supposing that the physical geometry on which matter dynamics take place could be Finslerian rather than just Riemannian. An appeal to the weak equivalence principle and causality then leads us the conclusion that the Finsler geometry has to reduce to a Riemann geometry whose metric - the physical metric - is related to the gravitational metric by a generalization of the conformal transformation.Comment: 15 pages, Te

Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice

`Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and to construct representations of Lie algebras on a lattice. Related ideas appeared in recent publications and we show that the examples treated there are special cases of umbral calculus. This observation then suggests various generalizations of these examples. A special umbral representation of the canonical commutation relations given in terms of the position and momentum operator on a lattice is investigated in detail.Comment: 19 pages, Late

Partonic description of a supersymmetric p-brane

We consider supersymmetric extensions of a recently proposed partonic description of a bosonic p-brane which reformulates the Nambu-Goto action as an interacting multi-particle action with Filippov-Lie algebra gauge symmetry. We construct a worldline supersymmetric action by postulating, among others, a p-form fermion. Demanding a local worldline supersymmetry rather than the full worldvolume supersymmetry, we circumvent a known no-go theorem against the construction of a Ramond-Neveu-Schwarz supersymmetric action for a p-brane of p>1. We also derive a spacetime supersymmetric Green-Schwarz extension from the preexisting kappa-symmetric action.Comment: 1+16 pages, no figure; References added and Concluding section expanded. Final version to appear in JHE

Opening the Treasure Chest: A Newborn Star Cluster Emerges from its Dust Pillar in Carina

We present detailed observations of the Treasure Chest, a compact nebula at the head of a dust pillar in the southern Carina nebula. This object is of interest because it is an example of a dense young cluster containing at least one massive star, the formation of which may have been triggered by feedback from the very massive stars in the Carina nebula, and possibly Eta Car itself. We investigate both the nebular and stellar content of the object. Near-IR emission-line images reveal a cavity inside the head of the dust pillar, which contains a dense cluster of young stars, while the observed spectrum of the nebula is consistent with an H II region ionized by an O9.5 V star. After subtracting contamination of field stars within the Carina nebula itself, we compare the cluster's color magnitude diagram with pre-main-sequence isochrones to derive a likely cluster age less than about 0.1 Myr. This is in reasonable agreement with the dynamical age of a few times 10^4 yr for the expanding nebular cavity, indicating extreme youth. Stars in the Treasure Chest cluster are highly reddened, with extinction values as large as A_V=50. Two-thirds of cluster members show strong infrared excess colors indicative of circumstellar disks, which may prove to be among the highest fraction yet seen for a young cluster. All evidence suggests that the Treaure Chest is an extremely young cluster that is just now breaking out of its natal cloud into the surrounding massive star forming region, and is a good target for more detailed study.Comment: 23 pages, 10 figs, 4 color fig

Gravitational Microlensing as a probe of the Electron Scattering Region in Q2237+0305

Recent observations have provided strong evidence for the presence of an Electron Scattering Region (ESR) within the central regions of AGNs. This is responsible for reprocessing emission from the accretion disk into polarised radiation. The geometry of this scattering region is, however, poorly constrained. In this paper, we consider the influence of gravitational microlensing on polarised emission from the ESR in the quadruply imaged quasar, Q2237+0305, demonstrating how correlated features in the resultant light curve variations can determine both the size and orientation of the scattering region. This signal is due to differential magnification between perpendicularly polarised views of the ESR, and is clearest for a small ESR width and a large ESR radius. Cross- and auto-correlation measures appear to be independent of lens image shear and convergence parameters, making it ideal to investigate ESR features. As with many microlensing experiments, the time-scale for variability, being of order decades to centuries, is impractically long. However, with a polarization filter oriented appropriately with respect to the path that the quasar takes across the caustic structure, the ESR diameter and radius can be estimated from the auto- and cross-correlation of polarized light curves on much shorter time-scales.Comment: 11 pages, 12 figures, 1 table, accepted for MNRA