Reduced classes and curve counting on surfaces II: calculations

We calculate the stable pair theory of a projective surface $S$. For fixed curve class $\beta\in H^2(S)$ the results are entirely topological, depending on $\beta^2$, $\beta.c_1(S)$, $c_1(S)^2$, $c_2(S)$, $b_1(S)$ \emph{and} invariants of the ring structure on $H^*(S)$ such as the Pfaffian of $\beta$ considered as an element of $\Lambda^2 H^1(S)^*$. Amongst other things, this proves an extension of the G\"ottsche conjecture to non-ample linear systems. We also give conditions under which this calculates the full 3-fold reduced residue theory of $K_S$. This is related to the reduced residue Gromov-Witten theory of $S$ via the MNOP conjecture. When the surface has no holomorphic 2-forms this can be expressed as saying that certain Gromov-Witten invariants of $S$ are topological. Our method uses the results of \cite{KT1} to express the reduced virtual cycle in terms of Euler classes of bundles over a natural smooth ambient space.Comment: 19 pages. Minor correction

Forecasting the money multiplier: implications for money stock control and economic activity

Forecasting ; Money supply

Accretion disk reversal and the spin-up/spin-down of accreting pulsars

We numerically investigate the hydrodynamics of accretion disk reversal and relate our findings to the observed spin-rate changes in the accreting X-ray pulsar GX~1+4. In this system, which accretes from a slow wind, the accretion disk contains two dynamically distinct regions. In the inner part viscous forces are dominant and disk evolution occurs on a viscous timescale. In the outer part dynamical mixing of material with opposite angular momentum is more important, and the externally imposed angular momentum reversal timescale governs the flow. In this outer region the disk is split into concentric rings of material with opposite senses of rotation that do not mix completely but instead remain distinct, with a clear gap between them. We thus predict that torque reversals resulting from accretion disk reversals will be accompanied by minima in accretion luminosity.Comment: 13 pages, 7 figures, accepted for publication in Ap

Using New Submillimetre Surveys to Identify the Evolutionary Status of High-z Galaxies

This paper describes a key submillimetre survey which we are currently conducting to address some of the outstanding questions in cosmology - how, at what epoch and over what period of time did massive galaxies form at high redshift? A summary of the technical feasibility of future submillimetre observations with new ground-based, airborne and satellite telescopes is also presented.Comment: 6 pages, 3 postscript figures, LaTex uses Kluwer book style file crckapb10.sty, to appear in "Observational Cosmology with the New Radio Surveys", 13-15 January 1997, Puerto de la Cruz, Tenerife, M.Bremer, N.Jackson, I.Perez-Fournon (eds.), Kluwe

Verlinde formulae on complex surfaces: K-theoretic invariants

We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between $K$-theoretic Donaldson invariants studied by the first named author and Nakajima-Yoshioka and $K$-theoretic Vafa-Witten invariants introduced by Thomas and also studied by the first and second named authors. We verify our conjectures in many examples (e.g. on K3 surfaces).Comment: Published version. 37 page

Jet Acceleration by Tangled Magnetic Fields

We explore the possibility that extragalactic radio jets might be accelerated by highly disorganized magnetic fields that are strong enough to dominate the dynamics until the terminal Lorentz factor is reached. Following the twin-exhaust model by Blandford & Rees (1974), the collimation under this scenario is provided by the stratified thermal pressure from an external medium. The acceleration efficiency then depends on the pressure gradient of that medium. In order for this mechanism to work there must be continuous tangling of the magnetic field, changing the magnetic equation of state away from pure flux freezing (otherwise conversion of Poynting flux to kinetic energy flux is suppressed). This is a complementary approach to models in which the plasma is accelerated by large scale ordered fields. We include a simple prescription for magnetic dissipation, which leads to tradeoffs among conversion of magnetic energy into bulk kinetic energy, random particle energy, and radiation. We present analytic dynamical solutions of such jets, assess the effects of radiation drag, and comment on observational issues, such as the predicted polarization and synchrotron brightness. Finally, we try to make the connection to observed radio galaxies and gamma-ray bursts.Comment: 15 pages, 10 figures, accepted for publication in Ap

Orbital Parameters and Chemical Composition of Four White Dwarfs in Post-Common Envelope Binaries

We present FUSE observations of the hot white dwarfs in the post-common envelope binaries Feige 24, EUVE J0720-317, BPM 6502, and EUVE J2013+400. The spectra show numerous photospheric absorption lines which trace the white dwarf orbital motion. We report the detection of C III, O VI, P V, and Si IV in the spectra of Feige 24, EUVE J0720-317 and EUVE J2013+400, and the detection of C III, N II, Si III, Si IV, and Fe III in the spectra of BPM 6502. Abundance measurements support the possibility that white dwarfs in post-common envelope binaries accrete material from the secondary star wind. The FUSE observations of BPM 6502 and EUVE J2013+400 cover a complete binary orbit. We used the FUSE spectra to measure the radial velocities traced by the white dwarf in the four binaries, where the zero-point velocity were fixed using the ISM velocities in the line of sight of the stellar systems. For BPM 6502 we determined a white dwarf velocity semi-amplitude of K_WD = 18.6+/-0.5km/s, and with the velocity semi-amplitude of the red dwarf companion (K_RD = 75.2+/-3.1 km/s), we estimate the mass ratio to be q = 0.25+/-0.01. Adopting a spectroscopic mass determination for the white dwarf, we infer a low secondary mass of M_RD = 0.14+/-0.01 M_solar. For EUVE J2013+400 we determine a white dwarf velocity semi-amplitude of K_WD = 36.7+/-0.7 km/s. The FUSE observations of EUVE J0720-317 cover approximately 30% of the binary period and combined with the HST GHRS measurements (Vennes et al. 1999, ApJ 523, 386), we update the binary properties. FUSE observations of Feige 24 cover approximately 60% of the orbit and we combine this data set with HST STIS (Vennes et al. 2000, ApJ, 544, 423) data to update the binary properties.Comment: Accepted for publication in Ap