Principles of Discrete Time Mechanics: IV. The Dirac Equation, Particles and Oscillons

We apply the principles of discrete time mechanics discussed in earlier papers to the first and second quantised Dirac equation. We use the Schwinger action principle to find the anticommutation relations of the Dirac field and of the particle creation operators in the theory. We find new solutions to the discrete time Dirac equation, referred to as oscillons on account of their extraordinary behaviour. Their principal characteristic is that they oscillate with a period twice that of the fundamental time interval T of our theory. Although these solutions can be associated with definite charge, linear momentum and spin, such objects should not be observable as particles in the continuous time limit. We find that for non-zero T they correspond to states with negative squared norm in Hilbert space. However they are an integral part of the discrete time Dirac field and should play a role in particle interactions analogous to the role of longitudinal photons in conventional quantum electrodynamics.Comment: 27 pages LateX; published versio

Magnetic Cataclysmic Variable Accretion Flows

We have used a magnetic accretion model to investigate the accretion flows of magnetic cataclysmic variables (mCVs) throughout a range of parameter space. The results of our numerical simulations demonstrate that broadly four types of flow are possible: discs, streams, rings and propellers. We show that the equilibrium spin periods in asynchronous mCVs, for a given orbital period and magnetic moment, occur where the flow changes from a type characterised by spin-up (i.e. disc or stream) to one characterised by spin-down (i.e. propeller or ring). 'Triple points' occur in the plane of spin-to-orbital period ratio versus magnetic moment, at which stream-disc-propeller flows or stream-ring-propeller flows can co-exist. The first of these is identified as corresponding to when the corotation radius is equal to the circularisation radius, and the second as where the corotation radius is equal to the distance from white dwarf to the L1 point. If mCVs are accreting at their equilibrium spin rates, then for a mass ratio of 0.5, those with Pspin/Porb < 0.1 will be disc-like, those with 0.1 < Pspin/Porb < 0.5 will be stream-like, and those with Pspin/Porb ~ 0.5 will be ring-like. In each case, some material is also lost from the binary in order to maintain angular momentum balance. The spin to orbital period ratio at which the systems transition between these flow types decreases as the mass ratio of the stellar components increases, and vice versa

Periodicities In The X-Ray Intensity Variations of TV Columbae: An Intermediate Polar

We present results from a temporal analysis of the longest and the most sensitive X-ray observations of TV Columbae--an intermediate polar. The observations were carried out with the RXTE PCA, ROSAT PSPC, and ASCA. Data were analyzed using a 1-dimensional CLEAN and Bayesian algorithms. The presence of a nearly sinusoidal modulation due to the spin of the white dwarf is seen clearly in all the data, confirming the previous reports based on the EXOSAT data. An improved period of 1909.7+/-2.5s is derived for the spin from the RXTE data.The binary period of 5.5hr is detected unambiguously in X-rays for the first time. Several side-bands due to the interaction of these periods are observed in the power spectra, thereby suggesting contributions from both the disk-fed and the stream-fed accretion for TV Col. The accretion disk could perhaps be precessing as side-bands due to the influence of 4 day period on the orbital period are seen. The presence of a significant power at certain side-bands of the spin frequency indicates that the emission poles are asymmetrically located. The strong power at the orbital side-bands seen in both the RXTE and ROSAT data gives an indication for an absorption site fixed in the orbital frame. Both the spin and the binary modulation are found to be energy-dependent. Increased hardness ratio during a broad dip in the intensity at binary phase of 0.75--1.0 confirms the presence of a strong attenuation due to additional absorbers probably from an impact site of the accretion stream with the disk or magnetosphere. Hardness ratio variations and the energy dependent modulation depth during the spin modulation can be explained by partially covered absorbers in the path of X-ray emission region in the accretion stream.Comment: 34 pages, including 12 figures, Accepted for publication in Astronomical Journal, scheduled for January 2004 issue (vol. 127

Export Tourism: Rejoinder to Palmer. Quarterly Economic Commentary, November 1983

There appear to be three central points in Noel Palmer's comments. These pertain to: I: The treatment of the government sector - should it be regarded as exogenous ( as in Norton, 1982) or endogenous? II: An assumtion of the input-output model used by me, namely, its failure to distinguish oetween average and marginal values of parameters. III: The relative capital intensity of export tourism

Evidence for polar jets as precursors of polar plume formation

Observations from the Hinode/XRT telescope and STEREO/SECCHI/EUVI are utilized to study polar coronal jets and plumes. The study focuses on the temporal evolution of both structures and their relationship. The data sample, spanning April 7-8 2007, shows that over 90% of the 28 observed jet events are associated with polar plumes. EUV images (STEREO/SECCHI) show plume haze rising from the location of approximately 70% of the polar X-ray (Hinode/XRT) and EUV jets, with the plume haze appearing minutes to hours after the jet was observed. The remaining jets occurred in areas where plume material previously existed causing a brightness enhancement of the latter after the jet event. Short-lived, jet-like events and small transient bright points are seen (one at a time) at different locations within the base of pre-existing long-lived plumes. X-ray images also show instances (at least two events) of collimated-thin jets rapidly evolving into significantly wider plume-like structures that are followed by the delayed appearance of plume haze in the EUV. These observations provide evidence that X-ray jets are precursors of polar plumes, and in some cases cause brightenings of plumes. Possible mechanisms to explain the observed jet and plume relationship are discussed.Comment: 10 pages, 4 figures, accepted as APJ Lette

The Accretion Flows and Evolution of Magnetic Cataclysmic Variables

We have used a model of magnetic accretion to investigate the accretion flows of magnetic cataclysmic variables. Numerical simulations demonstrate that four types of flow are possible: discs, streams, rings and propellers. The fundamental observable determining the accretion flow, for a given mass ratio, is the spin-to-orbital period ratio of the system. If IPs are accreting at their equilibrium spin rates, then for a mass ratio of 0.5, those with Pspin/Porb < 0.1 will be disc-like, those with 0.1 < Pspin/Porb < 0.6 will be stream-like, and those with Pspin/Porb ~ 0.6 will be ring-like. The spin to orbital period ratio at which the systems transition between these flow types increases as the mass ratio of the stellar components decreases. For the first time we present evolutionary tracks of mCVs which allow investigation of how their accretion flow changes with time. As systems evolve to shorter orbital periods and smaller mass ratios, in order to maintain spin equilibrium, their spin-to-orbital period ratio will generally increase. As a result, the relative occurrence of ring-like flows will increase, and the occurrence of disc-like flows will decrease, at short orbital periods. The growing number of systems observed at high spin-to-orbital period ratios with orbital periods below 2h, and the observational evidence for ring-like accretion in EX Hya, are fully consistent with this picture.Comment: Accepted for publication in ApJ. 6 figures - included here at low resolutio