Local Geometric Invariants of Integrable Evolution Equations

The integrable hierarchy of commuting vector fields for the localized induction equation of 3D hydrodynamics, and its associated recursion operator, are used to generate families of integrable evolution equations which preserve local geometric invariants of the evolving curve or swept-out surface.Comment: 15 pages, AMSTeX file (to appear in Journal of Mathematical Physics

Homogeneous nucleation: Comparison between two theories

The classical nucleation theory of Becker, D\"{o}ring and Zeldovich is compared with the Langer coarse-grained field approach to the nucleation phenomenon. Both formalisms have been applied to the condensation from a supersaturated vapor. It is shown that the nucleation rate derived in the classical theory can be expressed in a form equivalent to that of the field nucleation theory. This equivalence serves as an explanation of the puzzling fact that the numerical predictions of both theories for condensation of Xe and CO$_2$ are almost identical though the standard analytical expressions for the nucleation rates are different. The results obtained can help to link the theories of nucleation and their approximations.Comment: 12 pages, LaTeX, no figure

Impulsive solar X-ray bursts. 4: Polarization, directivity and spectrum of the reflected and total bremsstrahlung radiation from a beam of electrons directed toward the photosphere

A Monte Carlo method is described for evaluation of the spectrum, directivity and polarization of X-rays diffusely reflected from stellar photospheres. the accuracy of the technique is evaluated through comparison with analytic results. Using the characteristics of the incident X-rays of the model for solar X-ray flares, the spectrum, directivity and polarization of the reflected and the total X-ray fluxes are evaluated. The results are compared with observations

Impulsive solar X-ray bursts. 3: Polarization and directivity of bremsstrahlung radiation from a beam of electrons directed toward the photosphere

The spectrum, directivity and state of polarization is presented of the bremsstrahlung radiation expected from a beam of high energy electrons spiraling along radial magnetic field lines toward the photosphere. The results are used for calculation of the characteristics of the reflected plus direct flux

Wind bubbles within H II regions around slowly moving stars

Interstellar bubbles around O stars are driven by a combination of the star's wind and ionizing radiation output. The wind contribution is uncertain because the boundary between the wind and interstellar medium is difficult to observe. Mid-infrared observations (e.g., of the H II region RCW 120) show arcs of dust emission around O stars, contained well within the H II region bubble. These arcs could indicate the edge of an asymmetric stellar wind bubble, distorted by density gradients and/or stellar motion. We present two-dimensional, radiation-hydrodynamics simulations investigating the evolution of wind bubbles and H II regions around massive stars moving through a dense (n=3000 cm^{-3}), uniform medium with velocities ranging from 4 to 16 km/s. The H II region morphology is strongly affected by stellar motion, as expected, but the wind bubble is also very aspherical from birth, even for the lowest space velocity considered. Wind bubbles do not fill their H II regions (we find filling factors of 10-20%), at least for a main sequence star with mass M~30 Msun. Furthermore, even for supersonic velocities the wind bow shock does not significantly trap the ionization front. X-ray emission from the wind bubble is soft, faint, and comes mainly from the turbulent mixing layer between the wind bubble and the H II region. The wind bubble radiates <1 per cent of its energy in X-rays; it loses most of its energy by turbulent mixing with cooler photoionized gas. Comparison of the simulations with the H II region RCW 120 shows that its dynamical age is <=0.4 Myr and that stellar motion <=4 km/s is allowed, implying that the ionizing source is unlikely to be a runaway star but more likely formed in situ. The region's youth, and apparent isolation from other O or B stars, makes it very interesting for studies of massive star formation and of initial mass functions.Comment: 14 pages, 11 figures, accepted for publication in Astronomy and Astrophysics (new version corrects an error in the simulation postprocessing, figs 6,7,11 are modified slightly, conclusions unchanged

Multi-phase-field analysis of short-range forces between diffuse interfaces

We characterize both analytically and numerically short-range forces between spatially diffuse interfaces in multi-phase-field models of polycrystalline materials. During late-stage solidification, crystal-melt interfaces may attract or repel each other depending on the degree of misorientation between impinging grains, temperature, composition, and stress. To characterize this interaction, we map the multi-phase-field equations for stationary interfaces to a multi-dimensional classical mechanical scattering problem. From the solution of this problem, we derive asymptotic forms for short-range forces between interfaces for distances larger than the interface thickness. The results show that forces are always attractive for traditional models where each phase-field represents the phase fraction of a given grain. Those predictions are validated by numerical computations of forces for all distances. Based on insights from the scattering problem, we propose a new multi-phase-field formulation that can describe both attractive and repulsive forces in real systems. This model is then used to investigate the influence of solute addition and a uniaxial stress perpendicular to the interface. Solute addition leads to bistability of different interfacial equilibrium states, with the temperature range of bistability increasing with strength of partitioning. Stress in turn, is shown to be equivalent to a temperature change through a standard Clausius-Clapeyron relation. The implications of those results for understanding grain boundary premelting are discussed.Comment: 24 pages, 28 figure

On the stability of bow shocks generated by red supergiants: the case of IRC-10414

In this Letter, we explore the hypothesis that the smooth appearance of bow shocks around some red supergiants (RSGs) might be caused by the ionization of their winds by external sources of radiation. Our numerical simulations of the bow shock generated by IRC-10414 (the first-ever RSG with an optically detected bow shock) show that the ionization of the wind results in its acceleration by a factor of two, which reduces the difference between the wind and space velocities of the star and makes the contact discontinuity of the bow shock stable for a range of stellar space velocities and mass-loss rates. Our best fit model reproduces the overall shape and surface brightness of the observed bow shock and suggests that the space velocity and mass-loss rate of IRC-10414 are $\approx$50 ${\rm km} \, {\rm s}^{-1}$ and $\approx$$10^{-6}$ $M_\odot \, {\rm yr}^{-1}$, respectively, and that the number density of the local ISM is $\approx$3 ${\rm cm}^{-3}$. It also shows that the bow shock emission comes mainly from the shocked stellar wind. This naturally explains the enhanced nitrogen abundance in the line-emitting material, derived from the spectroscopy of the bow shock. We found that photoionized bow shocks are $\approx$15$-$50 times brighter in optical line emission than their neutral counterparts, from which we conclude that the bow shock of IRC-10414 must be photoionized.Comment: 5 pages, 5 figures. Accepted for publication in MNRAS Letter

Instability driven formation of domains in the intermediate state of type-I superconductors

The formation of normal-state domains in type-I superconducting indium films is investigated using the high resolution magneto-optical imaging technique. The observed patterns consist of coexisting circular and lamellar normal-phase domains surrounded by the superconducting phase. The distribution of domain surface areas is found to exhibit a threshold, above which only the lamellar shape is observed. We show that this threshold coincides with the predicted critical surface area for the elongation instability of the circular shape. The partition of the normal phase into circular and lamellar domains is determined by the combined effects of the elongation instability and the penetration of magnetic flux by bursts at the early stage of pattern formation. It is not governed by mutual interactions between domains, as usually assumed for self-organized systems