Unified derivation of phase-field models for alloy solidification from a grand-potential functional

In the literature, two quite different phase-field formulations for the problem of alloy solidification can be found. In the first, the material in the diffuse interfaces is assumed to be in an intermediate state between solid and liquid, with a unique local composition. In the second, the interface is seen as a mixture of two phases that each retain their macroscopic properties, and a separate concentration field for each phase is introduced. It is shown here that both types of models can be obtained by the standard variational procedure if a grand-potential functional is used as a starting point instead of a free-energy functional. The dynamical variable is then the chemical potential instead of the composition. In this framework, a complete analogy with phase-field models for the solidification of a pure substance can be established. This analogy is then exploited to formulate quantitative phase-field models for alloys with arbitrary phase diagrams. The precision of the method is illustrated by numerical simulations with varying interface thickness.Comment: 36 pages, 1 figur

Spin Asymmetry and Gerasimov-Drell-Hearn Sum Rule for the Deuteron

An explicit evaluation of the spin asymmetry of the deuteron and the associated GDH sum rule is presented which includes photodisintegration, single and double pion and eta production as well. Photodisintegration is treated with a realistic retarded potential and a corresponding meson exchange current. For single pion and eta production the elementary operator from MAID is employed whereas for double pion production an effective Lagrangean approach is used. A large cancellation between the disintegration and the meson production channels yields for the explicit GDH integral a value of 27.31 $\mu$b to be compared to the sum rule value 0.65 $\mu$b.Comment: 4 pages, 5 figures, revtex

Models of OH Maser Variations in U Her

Arecibo spectra of the mainline OH maser emission from U Her over more than a decade show variations of the OH emission over these time scales. These observations are combined with high spatial resolution VLBA maps to investigate the causes of the variations in the velocities of the maser components. Global properties of the dust shell, such as accelerations, variations in the pump and shell-wide magnetic field changes are examined as possibilities, and eliminated. A possible solution to the problem involving plasma turbulence and the local magnetic field is introduced, and the relevant time scales of the turbulence are calculated. The turbulent velocity field yields time scales of the turbulence are calculated. The turbulent velocity field yields time scales that are too long (of order centuries), while the turbulent magnetic field produces variations on appropriate time scales of a few years. A line-of-sight model of the turbulence is developed and investigated. The complete exploration of this solution requires extensive theoretical and observational work. Possible avenues of investigation of the plasma turbulence model are presented.Comment: 23 pages, 17 figures, ApJ: accepted Sept, 199

Non-locality and Medium Effects in the Exclusive Photoproduction of Eta Mesons on Nuclei

A relativistic model for the quasifree exclusive photoproduction of $\eta$ mesons on nuclei is extended to include both non-local and medium effects. The reaction is assumed to proceed via the dominant contribution of the S$_{11}$(1535) resonance. The complicated integrals resulting from the non-locality are simplified using a modified version of a method given by Cooper and Maxwell. The non-locality effects are found to affect the magnitude of the cross section. Some possibilities reflecting the effects of the medium on the propagation and properties of the intermediate S$_{11}$ resonance are studied. The effects of allowing the S$_{11}$ to interact with the medium via mean field scalar and vector potentials are considered. Both broadening of width and reduction in mass of the resonance lead to a suppression of the calculated cross sections.Comment: 19 pages, 7 figure

CO in OH/IR stars close to the Galactic centre

Aims: A pilot project has been carried out to measure circumstellar CO emission from three OH/IR stars close to the Galactic centre. The intention was to find out whether it would be possible to conduct a large-scale survey for mass-loss rates using, for example, the Atacama Large Millimeter Array (ALMA). Such a survey would increase our understanding of the evolution of the Galactic bulge. Methods: Two millimetre-wave instruments were used: the Nobeyama Millimeter Array at 115 GHz and the Submillimeter Array at 230 GHz. An interferometer is necessary as a `spatial filter' in this region of space because of the confusion with interstellar CO emission. Results: Towards two of the stars, CO emission was detected with positions and radial velocities coinciding within the statistical errors with the corresponding data of the associated OH sources. However, for one of the stars the line profile is not what one expects for an unresolved expanding circumstellar envelope. We believe that this CO envelope is partially resolved and that this star therefore is a foreground star not belonging to the bulge. Conclusions: The results of the observations have shown that it is possible to detect line profiles of circumstellar CO from late-type stars both within and in the direction of the Galactic bulge. ALMA will be able to detect CO emission in short integrations with sensitivity sufficient to estimate mass-loss rates from a large number of such stars.Comment: 5 pages, 3 figure

Incoherent Photoproduction of η\eta-mesons from the Deuteron near Threshold

Incoherent photoproduction of the $\eta$-meson on the deuteron is studied for photon energies from threshold to 800 MeV. The dominant contribution, the $\gamma$N-$\eta$N amplitude, is described within an isobar model. The final state interaction derived from the CD-Bonn potential is included and found to be important for the description of the production cross section close to threshold. Possible effects from the $\eta N$ final state interaction are discussed.Comment: 11 pages, revtex, including 6 figure

Nuclear dependence of the coherent eta photoproduction reaction in a relativistic approach

We study the nuclear (or A) dependence of the coherent eta photoproduction reaction in a relativistic impulse approximation approach. We use a standard relativistic parameterization of the elementary amplitude, based on a set of four Lorentz- and gauge-invariant amplitudes, to calculate the coherent production cross section from He-4, C-12, and Ca-40. In contrast to nonrelativistic treatments, our approach maintains the full relativistic structure of the process. The nuclear structure affects the process through the ground-state tensor density. This density is sensitive to relativistic effects and depends on A in a different manner than the vector density used in nonrelativistic approaches. This peculiar dependence results in He-4 having a cross section significantly smaller than that of C-12---in contrast to existent nonrelativistic calculations. Distortion effects are incorporated through an eta-nucleus optical potential that is computed in a simple ``t rho'' approximation.Comment: 4 pages, 3 postscript figures. The replace is due to a misspelling in the Authors' lis

Influence of image segmentation on one-dimensional fluid dynamics predictions in the mouse pulmonary arteries

Computational fluid dynamics (CFD) models are emerging as tools for assisting in diagnostic assessment of cardiovascular disease. Recent advances in image segmentation has made subject-specific modelling of the cardiovascular system a feasible task, which is particularly important in the case of pulmonary hypertension (PH), which requires a combination of invasive and non-invasive procedures for diagnosis. Uncertainty in image segmentation can easily propagate to CFD model predictions, making uncertainty quantification crucial for subject-specific models. This study quantifies the variability of one-dimensional (1D) CFD predictions by propagating the uncertainty of network geometry and connectivity to blood pressure and flow predictions. We analyse multiple segmentations of an image of an excised mouse lung using different pre-segmentation parameters. A custom algorithm extracts vessel length, vessel radii, and network connectivity for each segmented pulmonary network. We quantify uncertainty in geometric features by constructing probability densities for vessel radius and length, and then sample from these distributions and propagate uncertainties of haemodynamic predictions using a 1D CFD model. Results show that variation in network connectivity is a larger contributor to haemodynamic uncertainty than vessel radius and length