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  • FLUID MECHANICS AND HEAT TRANSFER  (16)
  • SOLID-STATE PHYSICS  (13)
  • SPACE RADIATION  (8)
  • 1
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    Quadratic resonance in the three-dimensional oscillations of inviscid drops with surface tension (1986)
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    Publication Date: 2011-08-19
    Description: The moderate-amplitude, three-dimensional oscillations of an inviscid drop are described in terms of spherical harmonics. Specific oscillation modes are resonantly coupled by quadratic nonlinearities caused by inertia, capillarity, and drop deformation. The equations describing the interactions of these modes are derived from the variational principle for the appropriate Lagrangian by expressing the modal amplitudes to be functions of a slow time scale and by preaveraging the Lagrangian over the time scale of the primary oscillations. Stochastic motions are predicted for nonaxisymmetric deformations starting from most initial conditions, even those arbitrarily close to the axisymmetric shapes. The stochasticity is characterized by a redistribution of the energy contained in the initial deformation over all the degrees of freedom of the interacting modes.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physics of Fluids (ISSN 0031-9171); 29; 2788-279
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  • 2
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    Thermal-capillary analysis of Czochralski and liquid encapsulated Czochralski crystal growth (1986)
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    Publication Date: 2011-08-19
    Description: Results are presented from finite element analysis of the Czochralski (CZ) and Liquid Encapsulated Czochralski (LEC) crystal growth processes based on a thermal-capillary model which governs the heat transfer in the system simultaneously with setting the shapes of the melt/solid interface, the melt and encapsulant menisci, and the radius of a steadily growing crystal. Calculations are performed for the small-scale growth of silicon (CZ) and gallium arsenide (LEC). The effects of melt volume and crucible position relative to the heater on the radius of the crystal and the shape of the melt/solid interface are predicted for the CZ system, and the importance of including an accurate representation of the melt meniscus for modeling the process is demonstrated. The additional effect of an encapsulant layer on heat transfer is treated for the LEC method for the cases of totally transparent and opaque encapsulant. The responses of these LEC prototype systems are examined for changes in pull rate and encapsulant volume.
    Keywords: SOLID-STATE PHYSICS
    Type: Journal of Crystal Growth (ISSN 0022-0248); 74; 605-624
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  • 3
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    Thermal-capillary analysis of Czochralski and liquid encapsulated Czochralski crystal growth. II - Processing strategies (1986)
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    Publication Date: 2011-08-19
    Description: The pseudosteady-state heat transfer model developed in a previous paper is augmented with constraints for constant crystal radius and melt/solid interface deflection. Combinations of growth rate, and crucible and bottom-heater temperatures are tested as processing parameters for satisfying the constrained thermal-capillary problem over a range of melt volumes corresponding to the sequence occuring during the batchwise Czochralski growth of a small-diameter silicon crystal. The applicability of each processing strategy is judged by the range of existence of the solution, in terms of melt volume and the values of the axial and radial temperature gradients in the crystal.
    Keywords: SOLID-STATE PHYSICS
    Type: Journal of Crystal Growth (ISSN 0022-0248); 75; 227-240
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  • 4
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    The role of three-dimensional shapes in the break-up of charged drops (1987)
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    Publication Date: 2011-08-19
    Description: The nonlinear dynamics of nonaxisymmetric inviscid charged conducting drops near the Rayleigh charge limit (R = 4) is investigated analytically. It is shown that only axisymmetric spheroid drops bifurcate from the sphere family when the charge is increased, that oblate spheroids at R greater than 4 are unstable to nonaxisymmetric disturbances governing drop breakup, and that prolate spheroids at R less than 4 are unstable only to axisymmetric disturbances tending to increase the length of the drop along its symmetry axis. The effects of external electric fields and rigid-body rotation are also analyzed, and the solutions for the amplitude equations at R just less than 4 (equivalent to the dynamical equations of the Henon-Heiles Hamiltonian) are explored.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Proceedings, Series A - Mathematical and Physical Sciences (ISSN 0080-4630); 410; 1838,; 209-227
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  • 5
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    Bifurcation structure and the Eckhaus instability (1989)
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    Publication Date: 2011-08-19
    Description: The bifurcation diagram corresponding to the Eckhaus stability curve has been constructed for the one-dimensional Swift-Hohenberg equation in a finite domain. Finite-amplitude solutions with particular spatial wavelength recover linear stability, as predicted by the Eckhaus curve, after a sequence of secondary bifurcations from the branch of solutions with this wavelength. No connectivity between the primary-solution branches is admissible if the stability predicted by this bifurcation diagram is to correspond to the prediction of the Eckhaus analysis. The Eckhaus curve does not exist if nonlinear couplings destroy this pattern. This is demonstrated by analysis of a coupled pair of Swift-Hohenberg equations.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physical Review Letters (ISSN 0031-9007); 63; 2048-205
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  • 6
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    Thermal-capillary analysis of small-scale floating zones Steady-state calculations (1986)
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    Publication Date: 2011-08-19
    Description: Galerkin finite element analysis of a thermal-capillary model of the floating zone crystal growth process is used to predict the dependence of molten zone shape on operating conditions for the growth of small silicon boules. The model accounts for conduction-dominated heat transport in the melt, feed rod and growing crystal and for radiation between these phases, the ambient and a heater. Surface tension acting on the shape of the melt/gas meniscus counteracts gravity to set the shape of the molten zone. The maximum diameter of the growing crystal is set by the dewetting of the melt from the feed rod when the crystal radius is large. Calculations with small Bond number show the increased zone lengths possible for growth in a microgravity environment. The sensitivity of the method to the shape and intensity of the applied heating distribution is demonstrated. The calculations are compared with experimental observations.
    Keywords: SOLID-STATE PHYSICS
    Type: Journal of Crystal Growth (ISSN 0022-0248); 75; 367-389
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  • 7
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    New class of asymmetric shapes of rotating liquid drops (1980)
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    Publication Date: 2011-08-17
    Description: Shapes and stability of surface-tension-endowed drops rotating rigidly at fixed angular momentum are calculated by finite-element analysis. A new family of asymmetric two-lobed drop shapes is discovered that branches from, and rejoins, the Pik-Pichak family of symmetric two-lobed shapes. The computations are verified for axisymmetric and symmetric two-lobed drop shape by comparison with previous approximations.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physical Review Letters; 45; July 21
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  • 8
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    Flow in a differentially rotated cylindrical drop at moderate Reynolds number (1984)
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    Publication Date: 2011-08-18
    Description: Galerkin finite-element approximations are combined with computer-implemented perturbation methods for tracking families of solutions to calculate the steady axisymmetric flows in a differentially rotated cylindrical drop as a function of Reynolds number Re, drop aspect ratio and the rotation ratio between the two end disks. The flows for Reynolds numbers below 100 are primarily viscous and reasonably described by an asymptotic analysis. When the disks are exactly counter-rotated, multiple steady flows are calculated that bifurcate to higher values of Re from the expected solution with two identical secondary cells stacked symmetrically about the axial midplane. The new flows have two cells of different size and are stable beyond the critical value Re sub c. The slope of the locus of Re sub c for drops with aspect ratio up to 3 disagrees with the result for two disks of infinite radius computed assuming the similarity form of the velocity field. Changing the rotation ratio for exact counter-rotation ruptures the junction of the multiple flow fields into two separated flow families.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Fluid Mechanics (ISSN 0022-1120); 144; 403-418
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  • 9
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    Finite element calculation of buoyancy-driven convection near a melt/solid phase boundary (1983)
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    Publication Date: 2011-08-18
    Description: Two iterative schemes based on the mixed finite element method are developed for analyzing steady natural convection in a melt adjacent to its solid phase. The simplest method decouples the calculation of the field variables and the shape of the melt/solid interface into two interlocked iterations that are performed successively. The second method uses Newton's iteration to solve simultaneously for both types of unknowns and has a quadratic convergence rate. Results for a model problem of melt and solid in a cylindrical ampoule show the Newton algorithm to be a factor of three more efficient.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
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  • 10
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    Natural convection in steady solidification - Finite element analysis of a two-phase Rayleigh-Benard problem (1984)
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    Publication Date: 2011-08-18
    Description: Galerkin finite-element approximations and Newton's method for solving free boundary problems are combined with computer-implemented techniques from nonlinear perturbation analysis to study solidification problems with natural convection in the melt. The Newton method gives rapid convergence to steady state velocity, temperature and pressure fields and melt-solid interface shapes, and forms the basis for algebraic methods for detecting multiple steady flows and assessing their stability. The power of this combination is demonstrated for a two-phase Rayleigh-Benard problem composed of melt and solid in a veritical cylinder with the thermal boundary conditions arranged so that a static melt with a flat melt-solid interface is always a solution. Multiple cellular flows bifurcating from the static state are detected and followed as Rayleigh number is varied. Changing the boundary conditions to approach those appropriate for the vertical Bridgman solidification system causes imperfections that eliminate the static state. The flow structure in the Bridgman system is related to those for the Rayleigh-Benard system by a continuous evolution of the boundary conditions.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Computational Physics (ISSN 0021-9991); 53; 1-27
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