Variational data assimilation for the initial-value dynamo problem

The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries

Expressing disambiguation filters as combinators

Contrarily to most conventional programming languages where certain symbols are used so as to create non-ambiguous grammars, most recent programming languages allow ambiguity. These ambiguities are solved using disambiguation rules, which dictate how the software that parses these languages should behave when faced with ambiguities. Such rules are highly efficient but come with some limitations - they cannot be further modified, their behaviour is hidden, and changing them implies re-building a parser. We propose a different approach for disambiguation. A set of disambiguation filters (expressed as combinators) are provided, and disambiguation can be achieved by composing combinators. New combinators can be created and, by having the disambiguation step separated from the parsing step, disambiguation rules can be changed without modifying the parser.- (undefined

PKS 1830-211: A Possible Compound Gravitational Lens

Measurements of the properties of gravitational lenses have the power to tell us what sort of universe we live in. The brightest known radio Einstein ring/gravitational lens PKS 1830-211 (Jauncey et al., 1991), whilst obscured by our Galaxy at optical wavelengths, has recently been shown to contain absorption at the millimetre waveband at a redshift of 0.89 (Wiklind and Combes, 1996a). We report the detection of a new absorption feature, most likely due to neutral hydrogen in a second redshift system at z = 0.19. Follow-up VLBI observations have spatially resolved the absorption and reveal it to cover the NE compact component and part of the lower surface brightness ring. This new information, together with existing evidence of the unusual VLBI radio structure and difficulties in modeling the lensing system, points to the existence of a second lensing galaxy along our line of sight and implies that PKS 1830-211 may be a compound gravitational lens.Comment: 8 pages, 2 figures, LaTeX (aasms4.sty). Accepted for publication in ApJ Letters. Preprint also available at http://kerr.phys.utas.edu.au/preprints

Optimized Discretization of Sources Imaged in Heavy-Ion Reactions

We develop the new method of optimized discretization for imaging the relative source from two particle correlation functions. In this method, the source resolution depends on the relative particle separation and is adjusted to available data and their errors. We test the method by restoring assumed pp sources and then apply the method to pp and IMF data. In reactions below 100 MeV/nucleon, significant portions of the sources extend to large distances (r > 20 fm). The results from the imaging show the inadequacy of common Gaussian source-parametrizations. We establish a simple relation between the height of the pp correlation function and the source value at short distances, and between the height and the proton freeze-out phase-space density.Comment: 36 pages (inc. 9 figures), RevTeX, uses epsf.sty. Submitted to Phys. Rev.

The effect of foot type of normal subjects on foot contact dynamics

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Helioseismic analysis of the hydrogen partition function in the solar interior

The difference in the adiabatic gradient gamma_1 between inverted solar data and solar models is analyzed. To obtain deeper insight into the issues of plasma physics, the so-called ``intrinsic'' difference in gamma_1 is extracted, that is, the difference due to the change in the equation of state alone. Our method uses reference models based on two equations of state currently used in solar modeling, the Mihalas-Hummer-Dappen (MHD) equation of state, and the OPAL equation of state (developed at Livermore). Solar oscillation frequencies from the SOI/MDI instrument on board the SOHO spacecraft during its first 144 days in operation are used. Our results confirm the existence of a subtle effect of the excited states in hydrogen that was previously studied only theoretically (Nayfonov & Dappen 1998). The effect stems from internal partition function of hydrogen, as used in the MHD equation of state. Although it is a pure-hydrogen effect, it takes place in somewhat deeper layers of the Sun, where more than 90% of hydrogen is ionized, and where the second ionization zone of helium is located. Therefore, the effect will have to be taken into account in reliable helioseismic determinations of the astrophysically relevant helium-abundance of the solar convection zone.Comment: 30 pages, 4 figures, 1 table. Revised version submitted to Ap

Stellar Inversion Techniques

Stellar seismic inversions have proved to be a powerful technique for probing the internal structure of stars, and paving the way for a better understanding of the underlying physics by revealing some of the shortcomings in current stellar models. In this lecture, we provide an introduction to this topic by explaining kernel-based inversion techniques. Specifically, we explain how various kernels are obtained from the pulsation equations, and describe inversion techniques such as the Regularised Least-Squares (RLS) and Optimally Localised Averages (OLA) methods.Comment: 20 pages, 8 figures. Lecture presented at the IVth Azores International Advanced School in Space Sciences on "Asteroseismology and Exoplanets: Listening to the Stars and Searching for New Worlds" (arXiv:1709.00645), which took place in Horta, Azores Islands, Portugal in July 201