Resonant Absorption as Mode Conversion? II. Temporal Ray Bundle

A fast-wave pulse in a simple, cold, inhomogeneous MHD model plasma is constructed by Fourier superposition over frequency of harmonic waves that are singular at their respective Alfven resonances. The pulse partially reflects before reaching the resonance layer, but also partially tunnels through to it to mode convert to an Alfven wave. The exact absorption/conversion coefficient for the pulse is shown to be given precisely by a function of transverse wavenumber tabulated in Paper I of this sequence, and to be independent of frequency and pulse width.Comment: 6 pages, 4 figures, accepted (15 Nov 2010) by Solar Physics. Ancillary file (animation) attache

Bound state spectra of three-body muonic molecular ions

The results of highly accurate calculations are presented for all twenty-two known bound $S(L = 0)-, P(L = 1)-, D(L = 2)-$ and $F(L = 3)-$states in the six three-body muonic molecular ions $pp\mu, pd\mu, pt\mu, dd\mu, dt\mu$ and $tt\mu$. A number of bound state properties of these muonic molecular ions have been determined numerically to high accuracy. The dependence of the total energies of these muonic molecules upon particle masses is considered. We also discuss the current status of muon-catalysis of nuclear fusion reactions.Comment: This is the final version. All `techical' troubles with the Latex-file have been resolved. A few misprints/mistakes in the text were correcte

On the Numerical Evaluation of One-Loop Amplitudes: the Gluonic Case

We develop an algorithm of polynomial complexity for evaluating one-loop amplitudes with an arbitrary number of external particles. The algorithm is implemented in the Rocket program. Starting from particle vertices given by Feynman rules, tree amplitudes are constructed using recursive relations. The tree amplitudes are then used to build one-loop amplitudes using an integer dimension on-shell cut method. As a first application we considered only three and four gluon vertices calculating the pure gluonic one-loop amplitudes for arbitrary external helicity or polarization states. We compare our numerical results to analytical results in the literature, analyze the time behavior of the algorithm and the accuracy of the results, and give explicit results for fixed phase space points for up to twenty external gluons.Comment: 22 pages, 9 figures; v2: references added, version accepted for publicatio

Fast computation of Bernoulli, Tangent and Secant numbers

We consider the computation of Bernoulli, Tangent (zag), and Secant (zig or Euler) numbers. In particular, we give asymptotically fast algorithms for computing the first n such numbers in O(n^2.(log n)^(2+o(1))) bit-operations. We also give very short in-place algorithms for computing the first n Tangent or Secant numbers in O(n^2) integer operations. These algorithms are extremely simple, and fast for moderate values of n. They are faster and use less space than the algorithms of Atkinson (for Tangent and Secant numbers) and Akiyama and Tanigawa (for Bernoulli numbers).Comment: 16 pages. To appear in Computational and Analytical Mathematics (associated with the May 2011 workshop in honour of Jonathan Borwein's 60th birthday). For further information, see http://maths.anu.edu.au/~brent/pub/pub242.htm

Scaling analysis of a divergent prefactor in the metastable lifetime of a square-lattice Ising ferromagnet at low temperatures

We examine a square-lattice nearest-neighbor Ising quantum ferromagnet coupled to $d$-dimensional phonon baths. Using the density-matrix equation, we calculate the transition rates between configurations, which determines the specific dynamic. Applying the calculated stochastic dynamic in Monte Carlo simulations, we measure the lifetimes of the metastable state. As the magnetic field approaches $|H|/J=2$ at low temperatures, the lifetime prefactor diverges because the transition rates between certain configurations approaches zero under these conditions. Near $|H|/J=2$ and zero temperature, the divergent prefactor shows scaling behavior as a function of the field, temperature, and the dimension of the phonon baths. With proper scaling, the simulation data at different temperatures and for different dimensions of the baths collapse well onto two master curves, one for $|H|/J>2$ and one for $|H|/J<2$.Comment: published versio

Resonant Absorption as Mode Conversion?

Resonant absorption and mode conversion are both extensively studied mechanisms for wave "absorption" in solar magnetohydrodynamics (MHD). But are they really distinct? We re-examine a well-known simple resonant absorption model in a cold MHD plasma that places the resonance inside an evanescent region. The normal mode solutions display the standard singular resonant features. However, these same normal modes may be used to construct a ray bundle which very clearly undergoes mode conversion to an Alfv\'en wave with no singularities. We therefore conclude that resonant absorption and mode conversion are in fact the same thing, at least for this model problem. The prime distinguishing characteristic that determines which of the two descriptions is most natural in a given circumstance is whether the converted wave can provide a net escape of energy from the conversion/absorption region of physical space. If it cannot, it is forced to run away in wavenumber space instead, thereby generating the arbitrarily small scales in situ that we recognize as fundamental to resonant absorption and phase mixing. On the other hand, if the converted wave takes net energy way, singularities do not develop, though phase mixing may still develop with distance as the wave recedes.Comment: 23 pages, 8 figures, 2 tables; accepted by Solar Phys (July 9 2010

Supersymmetric Euler-Heisenberg effective action: Two-loop results

The two-loop Euler-Heisenberg-type effective action for N = 1 supersymmetric QED is computed within the background field approach. The background vector multiplet is chosen to obey the constraints D_\a W_\b = D_{(\a} W_{\b)} = const, but is otherwise completely arbitrary. Technically, this calculation proves to be much more laborious as compared with that carried out in hep-th/0308136 for N = 2 supersymmetric QED, due to a lesser amount of supersymmetry. Similarly to Ritus' analysis for spinor and scalar QED, the two-loop renormalisation is carried out using proper-time cut-off regularisation. A closed-form expression is obtained for the holomorphic sector of the two-loop effective action, which is singled out by imposing a relaxed super self-duality condition.Comment: 27 pages, 2 eps figures, LaTeX; V2: typos corrected, comments and reference adde

CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes

We present a program that implements the OPP reduction method to extract the coefficients of the one-loop scalar integrals from a user defined (sub)-amplitude or Feynman Diagram, as well as the rational terms coming from the 4-dimensional part of the numerator. The rational pieces coming from the epsilon-dimensional part of the numerator are treated as an external input, and can be computed with the help of dedicated tree-level like Feynman rules. Possible numerical instabilities are dealt with the help of arbitrary precision routines, that activate only when needed.Comment: Version published in JHE

Disease and pharmacologic risk factors for first and subsequent episodes of equine laminitis: a cohort study of free-text electronic medical records

Electronic medical records from first opinion equine veterinary practice may represent a unique resource for epidemiologic research. The appropriateness of this resource for risk factor analyses was explored as part of an investigation into clinical and pharmacologic risk factors for laminitis. Amalgamated medical records from seven UK practices were subjected to text mining to identify laminitis episodes, systemic or intra-synovial corticosteroid prescription, diseases known to affect laminitis risk and clinical signs or syndromes likely to lead to corticosteroid use. Cox proportional hazard models and Prentice, Williams, Peterson models for repeated events were used to estimate associations with time to first, or subsequent laminitis episodes, respectively. Over seventy percent of horses that were diagnosed with laminitis suf- fered at least one recurrence. Risk factors for first and subsequent laminitis episodes were found to vary. Corticosteroid use (prednisolone only) was only significantly associated with subsequent, and not ini- tial laminitis episodes. Electronic medical record use for such analyses is plausible and offers important advantages over more traditional data sources. It does, however, pose challenges and limitations that must be taken into account, and requires a conceptual change to disease diagnosis which should be considered carefully