Coupling iterated Kolmogorov diffusions

The Kolmogorov (1934) diffusion is the two-dimensional diffusion generated by real Brownian motion B and its time integral integral B d t. In this paper we construct successful co-adapted couplings for iterated Kolmogorov diffusions defined by adding iterated time integrals integral integral B d s d t,... as further components to the original Kolmogorov diffusion. A Laplace-transform argument shows it is not possible successfully to couple all iterated time integrals at once; however we give an explicit construction of a successful co-adapted coupling method for (B, integral B d t, integral integral B d s d t); and a more implicit construction of a successful co-adapted coupling method which works for finite sets of iterated time integrals

Photoproduction of Xi off nucleons

The photoproduction reaction $\gamma N \to K K \Xi$ is investigated based on a relativistic meson-exchange model of hadronic interactions. The production amplitude is calculated in the tree-level approximation from relevant effective Lagrangians, whose (coupling constant) parameters are mostly fixed from the empirical data and/or quark models together with SU(3) symmetry considerations. Gauge invariance of the resulting amplitude is maintained by introducing the contact currents by extending the gauge-invariant approach of Haberzettl for one-meson photoproduction to two-meson photoproduction. The role of the intermediate low-lying hyperons and of the intermediate higher-mass hyperon resonances are analyzed in detail. In particular, the basic features of the production of $\Xi^-(1318)$ in $\gamma p \to K^+ K^+ \Xi^-$ and their possible manifestations in the forthcoming experimental data are discussed.Comment: 18 pages, 17 figures, REVTeX, 1 figure added, to appear in Phys. Rev.

Molecules, ices and astronomy

Molecules in interstellar gas and in interstellar ices play a fundamental role in astronomy. However, the formation of the simplest molecule, molecular hydrogen, is still not fully understood. Similarly, although interstellar ice analogues have received much attention in the laboratory, the evolution of ices in the interstellar medium still requires further study. At UCL we have developed two separate experiments to address these issues and explore the following questions: How is H formed on dust-grain surfaces? What is the budget between internal, kinetic and surface energies in the formation process? What are the astronomical consequences of these results? For ices, we ask: How do molecules desorb from pure and from mixed ices in regions warmed by newly formed stars? What can molecules released from ices tell us about the star-formation process? We put our results in the context of other laboratory work and we describe their application to current problems in astronomy

Pre- and Post-selection paradoxes and contextuality in quantum mechanics

Many seemingly paradoxical effects are known in the predictions for outcomes of intermediate measurements made on pre- and post-selected quantum systems. Despite appearances, these effects do not demonstrate the impossibility of a noncontextual hidden variable theory, since an explanation in terms of measurement-disturbance is possible. Nonetheless, we show that for every paradoxical effect wherein all the pre- and post- selected probabilities are 0 or 1 and the pre- and post-selected states are nonorthogonal, there is an associated proof of contextuality. This proof is obtained by considering all the measurements involved in the paradoxical effect -- the pre-selection, the post-selection, and the alternative possible intermediate measurements -- as alternative possible measurements at a single time.Comment: 5 pages, 1 figure. Submitted to Phys. Rev. Lett. v2.0 revised in the light of referee comments, results unchange

Periodic Solutions of the Einstein Equations for Binary Systems

This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with outgoing waves. A variational principle is found which has the power to provide an accurate estimate of the relationship between the mass and angular momentum of the system, the masses and angular momenta of the components, the rotational frequency of the frame of reference in which the system is periodic, the frequency of the periodicity of the system, and the amplitude and phase of each multipole component of gravitational radiation. Examination of the boundary terms of the variational principle leads to definitions of the effective mass and effective angular momentum of a periodic geometry which capture the concepts of mass and angular momentum of the source alone with no contribution from the gravitational radiation. These effective quantities are surface integrals in the weak-field zone which are independent of the surface over which they are evaluated, through second order in the deviations of the metric from flat space.Comment: 18 pages, RevTeX 3.0, UF-RAP-93-1

Tidal interaction in binary black hole inspiral

In rotating viscous fluid stars, tidal torque leads to an exchange of spin and orbital angular momentum. The horizon of a black hole has an effective viscosity that is large compared to that of stellar fluids, and an effective tidal torque may lead to important effects in the strong field interaction at the endpoint of the inspiral of two rapidly rotating holes. In the most interesting case both holes are maximally rotating and all angular momenta (orbital and spins) are aligned. We point out here that in such a case (i) the transfer of angular momentum may have an important effect in modifying the gravitational wave ``chirp'' at the endpoint of inspiral. (ii) The tidal transfer of spin energy to orbital energy may increase the amount of energy being radiated. (iii) Tidal transfer in such systems may provide a mechanism for shedding excess angular momentum. We argue that numerical relativity, the only tool for determining the importance of tidal torque, should be more specifically focused on binary configurations with aligned, large, angular momenta.Comment: 5 pages, 2 figure

Formation of a rotating hole from a close limit head-on collision

Realistic black hole collisions result in a rapidly rotating Kerr hole, but simulations to date have focused on nonrotating final holes. Using a new solution of the Einstein initial value equations we present here waveforms and radiation for an axisymmetric Kerr-hole-forming collision starting from small initial separation (the ``close limit'' approximation) of two identical rotating holes. Several new features are present in the results: (i) In the limit of small separation, the waveform is linear (not quadratic) in the separation. (ii) The waveforms show damped oscillations mixing quasinormal ringing of different multipoles.Comment: 4 pages, 4 figures, submitted to PR

The Pan-STARRS1 Photometric System

The Pan-STARRS1 survey is collecting multi-epoch, multi-color observations of the sky north of declination -30 deg to unprecedented depths. These data are being photometrically and astrometrically calibrated and will serve as a reference for many other purposes. In this paper we present our determination of the Pan-STARRS photometric system: gp1, rp1, ip1, zp1, yp1, and wp1. The Pan-STARRS photometric system is fundamentally based on the HST Calspec spectrophotometric observations, which in turn are fundamentally based on models of white dwarf atmospheres. We define the Pan-STARRS magnitude system, and describe in detail our measurement of the system passbands, including both the instrumental sensitivity and atmospheric transmission functions. Byproducts, including transformations to other photometric systems, galactic extinction, and stellar locus are also provided. We close with a discussion of remaining systematic errors.Comment: 39 pages, 9 figures, machine readable table of bandpasses, accepted for publication in Ap

Late-Time Evolution of Realistic Rotating Collapse and The No-Hair Theorem

We study analytically the asymptotic late-time evolution of realistic rotating collapse. This is done by considering the asymptotic late-time solutions of Teukolsky's master equation, which governs the evolution of gravitational, electromagnetic, neutrino and scalar perturbations fields on Kerr spacetimes. In accordance with the no-hair conjecture for rotating black-holes we show that the asymptotic solutions develop inverse power-law tails at the asymptotic regions of timelike infinity, null infinity and along the black-hole outer horizon (where the power-law behaviour is multiplied by an oscillatory term caused by the dragging of reference frames). The damping exponents characterizing the asymptotic solutions at timelike infinity and along the black-hole outer horizon are independent of the spin parameter of the fields. However, the damping exponents at future null infinity are spin dependent. The late-time tails at all the three asymptotic regions are spatially dependent on the spin parameter of the field. The rotational dragging of reference frames, caused by the rotation of the black-hole (or star) leads to an active coupling of different multipoles.Comment: 16 page