Analytical and numerical studies of the thermocapillary flow in a uniformly floating zone

The microgravity environment of an orbiting vehicle permits crystal growth experiments in the presence of greatly reduced buoyant convection in the liquid melt. Crystals grown in ground-based laboratories do not achieve their potential properties because of dopant variations caused by flow in the melt. The floating zone crystal growing system is widely used to produce crystals of silicon and other materials. However, in this system the temperature gradient on the free sidewall surface of the melt is the source of a thermocapillary flow which does not disappear in the low-gravity environment. The idea of using a uniform rotation of the floating zone system to confine the thermocapillary flow to the melt sidewall leaving the interior of the melt passive is examined. A cylinder of fluid with an axial temperature gradient imposed on the cylindrical sidewall is considered. A half zone and the linearized, axisymmetric flow in the absence of crystal growth is examined. Rotation is found to confine the linear thermocapillary flow. A simplified model is extended to a full zone and both linear and nonlinear thermocapillary flows are studied theoretically. Analytical and numerical methods are used for the linear flows and numerical methods for the nonlinear flows. It was found that the linear flows in the full zone have more complicated and thicker boundary layer structures than in the half zone, and that these flows are also confined by the rotation. However, for the simplified model considered and for realistic values for silicon, the thermocapillary flow is not linear. The fully nonlinear flow is strong and unsteady (a weak oscillation is present) and it penetrates the interior. Some non-rotating flow results are also presented. Since silicon as a large value of thermal conductivity, one would expect the temperature fields to be determined by conduction alone. This is true for the linear and weakly nonlinear flows, but for the stronger nonlinear flow the results show that temperature advection is also important. Uniform rotation may still be a means of confining the flow and the results obtained define the procedure to be used to examine this hypothesis

Numerical prediction of 3-D ejector flows

The use of parametric flow analysis, rather than parametric scale testing, to support the design of an ejector system offers a number of potential advantages. The application of available 3-D flow analyses to the design ejectors can be subdivided into several key elements. These are numerics, turbulence modeling, data handling and display, and testing in support of analysis development. Experimental and predicted jet exhaust for the Boeing 727 aircraft are examined

Collisional dynamics of perturbed particle disks in the solar system

Investigations of the collisional evolution of particulate disks subject to the gravitational perturbation of a more massive particle orbiting within the disk are underway. Both numerical N-body simulations using a novel collision algorithm and analytical kinetic theory are being employed to extend our understanding of perturbed disks in planetary rings and during the formation of the solar system. Particular problems proposed for investigation are: (1) The development and testing of general criteria for a small moonlet to clear a gap and produce observable morphological features in planetary rings; (2) The development of detailed models of collisional damping of the wavy edges observed on the Encke division of Saturn's A ring; and (3) The determination of the extent of runaway growth of the few largest planetesimals during the early stages of planetary accretion

The Transversal Relative Equilibria of a Hamiltonian System with Symmetry

We show that, given a certain transversality condition, the set of relative equilibria \mcl E near p_e\in\mcl E of a Hamiltonian system with symmetry is locally Whitney-stratified by the conjugacy classes of the isotropy subgroups (under the product of the coadjoint and adjoint actions) of the momentum-generator pairs $(\mu,\xi)$ of the relative equilibria. The dimension of the stratum of the conjugacy class (K) is $\dim G+2\dim Z(K)-\dim K$, where Z(K) is the center of K, and transverse to this stratum \mcl E is locally diffeomorphic to the commuting pairs of the Lie algebra of $K/Z(K)$. The stratum \mcl E_{(K)} is a symplectic submanifold of P near p_e\in\mcl E if and only if $p_e$ is nondegenerate and K is a maximal torus of G. We also show that there is a dense subset of G-invariant Hamiltonians on P for which all the relative equilibria are transversal. Thus, generically, the types of singularities that can be found in the set of relative equilibria of a Hamiltonian system with symmetry are those types found amongst the singularities at zero of the sets of commuting pairs of certain Lie subalgebras of the symmetry group.Comment: 18 page

The prevalence and properties of cold gas inflows and outflows around galaxies in the local Universe

We perform a stacking analysis of the neutral \nad\,$\lambda\lambda$5889,5895\,\AA\ ISM doublet using the SDSS DR7 spectroscopic data set to probe the prevalence and characteristics of cold (T\,$\lesssim$\,10$^{4}$\,K) galactic-scale gas flows in local (0.025$\leqslant z\leqslant$0.1) inactive and AGN-host galaxies across the SFR-M$_{*}$ plane. We find low-velocity outflows to be prevalent in regions of high SFRs and stellar masses (10 $\lesssim$log M$_{*}$/M$_{\odot}$ $\lesssim$ 11.5), however we do not find any detections in the low mass (log M$_{*}$/M$_{\odot}$ $\lesssim$ 10) regime. We also find tentative detections of inflowing gas in high mass galaxies across the star-forming population. We derive mass outflow rates in the range of 0.14-1.74\,M$_{\odot}$yr$^{-1}$ and upper limits on inflow rates <1\,M$_{\odot}$yr$^{-1}$, allowing us to place constraints on the mass loading factor ($\eta$=$\dot{M}_{\text{out}}$/SFR) for use in simulations of the local Universe. We discuss the fate of the outflows by comparing the force provided by the starburst to the critical force needed to push the outflow outward, and find the vast majority of the outflows unlikely to escape the host system. Finally, as outflow detection rates and central velocities do not vary strongly with the presence of a (weak) active supermassive black hole, we determine that star formation appears to be the primary driver of outflows at $z\sim$0.Comment: Accepted in MNRAS. 36 pages, 15 figure

Formation of giant molecular clouds in global spiral structures: The role of orbital dynamics and cloud-cloud collisions

The different roles played by orbital dynamics and dissipative cloud-cloud collisions in the formation of giant molecular clouds (GMCs) in a global spiral structure are investigated. The interstellar medium (ISM) is simulated by a system of particles, representing clouds, which orbit in a spiral-perturbed, galactic gravitational field. The overall magnitude and width of the global cloud density distribution in spiral arms is very similar in the collisional and collisionless simulations. The results suggest that the assumed number density and size distribution of clouds and the details of individual cloud-cloud collisions have relatively little effect on these features. Dissipative cloud-cloud collisions play an important steadying role for the cloud system's global spiral structure. Dissipative cloud-cloud collisions also damp the relative velocity dispersion of clouds in massive associations and thereby aid in the effective assembling of GMC-like complexes

The in-vacuo torque performance of dry-lubricated ball bearings at cryogenic temperatures

The performance of dry-lubricated, angular contact ball bearings in vacuum at a temperature of 20 degrees K has been investigated, and is compared with the in-vacuo performance at room temperatures. Bearings were lubricated using dry-lubricant techniques which have been previously established for space applications involving operations at or near room temperature. Comparative tests were undertaken using three lubricants: molybdenum disulphide, lead, and PTFE. Results obtained using the three lubricants are presented

Finite-difference fluid dynamics computer mathematical models for the design and interpretation of experiments for space flight

Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface

Interactions of vortices with rarefaction solitary waves in a Bose-Einstein condensate and their role in the decay of superfluid turbulence

There are several ways to create the vorticity-free solitary waves -- rarefaction pulses -- in condensates: by the process of strongly nonequilibrium condensate formation in a weakly interacting Bose gas, by creating local depletion of the condensate density by a laser beam, and by moving a small object with supercritical velocities. Perturbations created by such waves colliding with vortices are studied in the context of the Gross-Pitaevskii model. We find that the effect of the interactions consists of two competing mechanisms: the creation of vortex line as rarefaction waves acquire circulation in a vicinity of a vortex core and the loss of the vortex line to sound due to Kelvin waves that are generated on vortex lines by rarefaction pulses. When a vortex ring collides with a rarefaction wave, the ring either stabilises to a smaller ring after emitting sound through Kelvin wave radiation or the entire energy of the vortex ring is lost to sound if the radius of the ring is of the order of the healing length. We show that during the time evolution of a tangle of vortices, the interactions with rarefaction pulses provide an important dissipation mechanism enhancing the decay of superfluid turbulence.Comment: Revised paper accepted by Phys. Rev.