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

Frustrated Rotations in Nematic Monolayers

Tabe and Yokoyama found recently that the optical axis in a chiral monolayer of a ferronematic rotates when water evaporates from the bath: the chiral molecules act as propellers. When the axis is blocked at the lateral walls of the trough, the accumulated rotation inside creates huge splays and bends. We discuss the relaxation of these tensions, assuming that a single dust particle nucleates disclination pairs. For the simplest geometry, we then predict a long delay time followed by a non-periodic sequence of ``bursts''. These ideas are checked by numerical simulations.Comment: 5 pages, 4 figures, submitted to Eur. Phys. J.

Steady-state, effective-temperature dynamics in a glassy material

We present an STZ-based analysis of numerical simulations by Haxton and Liu (HL). The extensive HL data sharply test the basic assumptions of the STZ theory, especially the central role played by the effective disorder temperature as a dynamical state variable. We find that the theory survives these tests, and that the HL data provide important and interesting constraints on some of its specific ingredients. Our most surprising conclusion is that, when driven at various constant shear rates in the low-temperature glassy state, the HL system exhibits a classic glass transition, including super-Arrhenius behavior, as a function of the effective temperature.Comment: 9 pages, 6 figure

The State of the Circumstellar Medium Surrounding Gamma-Ray Burst Sources and its Effect on the Afterglow Appearance

We present a numerical investigation of the contribution of the presupernova ejecta of Wolf-Rayet stars to the environment surrounding gamma-ray bursts (GRBs), and describe how this external matter can affect the observable afterglow characteristics. An implicit hydrodynamic calculation for massive stellar evolution is used here to provide the inner boundary conditions for an explicit hydrodynamical code to model the circumstellar gas dynamics. The resulting properties of the circumstellar medium are then used to calculate the deceleration of a relativistic, gas-dynamic jet and the corresponding afterglow light curve produced as the shock wave propagates through the shocked-wind medium. We find that variations in the stellar wind drive instabilities that may produce radial filaments in the shocked-wind region. These comet-like tails of clumps could give rise to strong temporal variations in the early afterglow lightcurve. Afterglows may be expected to differ widely among themselves, depending on the angular anisotropy of the jet and the properties of the stellar progenitor; a wide diversity of behaviors may be the rule, rather than the exception.Comment: 17 pages, 7 figures, ApJ in pres

Binaries are the best single stars

Stellar models of massive single stars are still plagued by major uncertainties. Testing and calibrating against observations is essential for their reliability. For this purpose one preferably uses observed stars that have never experienced strong binary interaction, i.e. "true single stars". However, the binary fraction among massive stars is high and identifying "true single stars" is not straight forward. Binary interaction affects systems in such a way that the initially less massive star becomes, or appears to be, single. For example, mass transfer results in a widening of the orbit and a decrease of the luminosity of the donor star, which makes it very hard to detect. After a merger or disruption of the system by the supernova explosion, no companion will be present. The only unambiguous identification of "true single stars" is possible in detached binaries, which contain two main-sequence stars. For these systems we can exclude the occurrence of mass transfer since their birth. A further advantage is that binaries can often provide us with direct measurements of the fundamental stellar parameters. Therefore, we argue these binaries are worth the effort needed to observe and analyze them. They may provide the most stringent test cases for single stellar models.Comment: 5 pages, 1 figure, contribution to the proceedings of "The multi-wavelength view of hot, massive stars", 39th Li`ege Int. Astroph. Coll., 12-16 July 201

On the spectrum of the magnetohydrodynamic mean-field alpha^2-dynamo operator

The existence of magnetohydrodynamic mean-field alpha^2-dynamos with spherically symmetric, isotropic helical turbulence function alpha is related to a non-self-adjoint spectral problem for a coupled system of two singular second order ordinary differential equations. We establish global estimates for the eigenvalues of this system in terms of the turbulence function alpha and its derivative alpha'. They allow us to formulate an anti-dynamo theorem and a non-oscillation theorem. The conditions of these theorems, which again involve alpha and alpha', must be violated in order to reach supercritical or oscillatory regimes.Comment: 35 pages, 4 figures, to be published in SIAM J. Math. Anal

Separator development for a heat sterilizable battery Quarterly report, 1 Oct. - 31 Dec. 1966

Composite separator production for heat sterilizable silver-zinc batterie

Novel modelling of ultra-compact X-ray binary evolution - stable mass transfer from white dwarfs to neutron stars

Tight binaries of helium white dwarfs (He WDs) orbiting millisecond pulsars (MSPs) will eventually "merge" due to gravitational damping of the orbit. The outcome has been predicted to be the production of long-lived ultra-compact X-ray binaries (UCXBs), in which the WD transfers material to the accreting neutron star (NS). Here we present complete numerical computations, for the first time, of such stable mass transfer from a He WD to a NS. We have calculated a number of complete binary stellar evolution tracks, starting from pre-LMXB systems, and evolved these to detached MSP+WD systems and further on to UCXBs. The minimum orbital period is found to be as short as 5.6 minutes. We followed the subsequent widening of the systems until the donor stars become planets with a mass of ~0.005 Msun after roughly a Hubble time. Our models are able to explain the properties of observed UCXBs with high helium abundances and we can identify these sources on the ascending or descending branch in a diagram displaying mass-transfer rate vs. orbital period.Comment: 6 pages, 4 figures, MNRAS Letters, in pres

Separator development for a heat sterilizable battery Quarterly report, 1 Jun. - 30 Sep. 1966

Filler and matrix composite materials for use in silver-zinc battery separator