Techniques for evaluation of E-beam evaporative processes

High dynamic range video imaging of the molten pool surface has provided insight regarding process responses at the melt pool liquid-vapor interface. A water-cooled video camera provides continuous high resolution imaging of the pool surface from a low angle position within 20 cm of the liquid-vapor interface. From the vantage point, the e-beam footprint is clearly defined and melt pool free surface shape can be observed. Effects of changes in a beam footprint, power distribution, and sweep frequency on pool surface shape and stability of vaporization are immediately shown. Other events observed and recorded include: formation of the pool and dissipation of ``rafts`` on the pool surface during startup, behavior of feed material as it enters the pool, effects of feed configuration changes on mixing of feed entering the pool volume and behaviors of co-evaporated materials of different vapor pressures at the feed/pool boundary. When used in conjunction with laser vapor monitoring, correlation between pool surface phenomena and vaporizer performance has been identified. This video capability was used in verifying the titanium evaporation model results presented at this conference by confirming the calculated melt pool surface deformations caused by vapor pressure of the departing evaporant at the liquid-vapor interface

Topological Defects on Fluctuating Surfaces: General Properties and the Kosterlitz-Thouless Transition

We investigate the Kosterlitz-Thouless transition for hexatic order on a free fluctuating membrane and derive both a Coulomb gas and a sine-Gordon Hamiltonian to describe it. The Coulomb-gas Hamiltonian includes charge densities arising from disclinations and from Gaussian curvature. There is an interaction coupling the difference between these two densities, whose strength is determined by the hexatic rigidity, and an interaction coupling Gaussian curvature densities arising from the Liouville Hamiltonian resulting from the imposition of a covariant cutoff. In the sine-Gordon Hamiltonian, there is a linear coupling between a scalar field and the Gaussian curvature. We discuss gauge-invariant correlation function for hexatic order and the dielectric constant of the Coulomb gas. We also derive renormalization group recursion relations that predict a transition with decreasing bending rigidity $\kappa$.Comment: REVTEX, 45 pages with 11 postscript figures compressed using uufiles. Accepted for publication in Phys. Rev.

Quantum measurement in a family of hidden-variable theories

The measurement process for hidden-configuration formulations of quantum mechanics is analysed. It is shown how a satisfactory description of quantum measurement can be given in this framework. The unified treatment of hidden-configuration theories, including Bohmian mechanics and Nelson's stochastic mechanics, helps in understanding the true reasons why the problem of quantum measurement can succesfully be solved within such theories.Comment: 16 pages, LaTeX; all special macros are included in the file; a figure is there, but it is processed by LaTe

Analysis of Nematic Liquid Crystals with Disclination Lines

We investigate the structure of nematic liquid crystal thin films described by the Landau--de Gennes tensor-valued order parameter with Dirichlet boundary conditions of nonzero degree. We prove that as the elasticity constant goes to zero a limiting uniaxial texture forms with disclination lines corresponding to a finite number of defects, all of degree 1/2 or all of degree -1/2. We also state a result on the limiting behavior of minimizers of the Chern-Simons-Higgs model without magnetic field that follows from a similar proof.Comment: 40 pages, 1 figur

Equidistribution of zeros of holomorphic sections in the non compact setting

We consider N-tensor powers of a positive Hermitian line bundle L over a non-compact complex manifold X. In the compact case, B. Shiffman and S. Zelditch proved that the zeros of random sections become asymptotically uniformly distributed with respect to the natural measure coming from the curvature of L, as N tends to infinity. Under certain boundedness assumptions on the curvature of the canonical line bundle of X and on the Chern form of L we prove a non-compact version of this result. We give various applications, including the limiting distribution of zeros of cusp forms with respect to the principal congruence subgroups of SL2(Z) and to the hyperbolic measure, the higher dimensional case of arithmetic quotients and the case of orthogonal polynomials with weights at infinity. We also give estimates for the speed of convergence of the currents of integration on the zero-divisors.Comment: 25 pages; v.2 is a final update to agree with the published pape

A classical explanation of quantization

In the context of our recently developed emergent quantum mechanics, and, in particular, based on an assumed sub-quantum thermodynamics, the necessity of energy quantization as originally postulated by Max Planck is explained by means of purely classical physics. Moreover, under the same premises, also the energy spectrum of the quantum mechanical harmonic oscillator is derived. Essentially, Planck's constant h is shown to be indicative of a particle's "zitterbewegung" and thus of a fundamental angular momentum. The latter is identified with quantum mechanical spin, a residue of which is thus present even in the non-relativistic Schroedinger theory.Comment: 20 pages; version accepted for publication in Foundations of Physic

Replica Symmetry Breaking Instability in the 2D XY model in a random field

We study the 2D vortex-free XY model in a random field, a model for randomly pinned flux lines in a plane. We construct controlled RG recursion relations which allow for replica symmetry breaking (RSB). The fixed point previously found by Cardy and Ostlund in the glass phase $T<T_c$ is {\it unstable} to RSB. The susceptibility $\chi$ associated to infinitesimal RSB perturbation in the high-temperature phase is found to diverge as $\chi \propto (T-T_c)^{-\gamma}$ when $T \rightarrow T_c^{+}$. This provides analytical evidence that RSB occurs in finite dimensional models. The physical consequences for the glass phase are discussed.Comment: 8 pages, REVTeX, LPTENS-94/2

Thermodynamic Gravity and the Schrodinger Equation

We adopt a 'thermodynamical' formulation of Mach's principle that the rest mass of a particle in the Universe is a measure of its long-range collective interactions with all other particles inside the horizon. We consider all particles in the Universe as a 'gravitationally entangled' statistical ensemble and apply the approach of classical statistical mechanics to it. It is shown that both the Schrodinger equation and the Planck constant can be derived within this Machian model of the universe. The appearance of probabilities, complex wave functions, and quantization conditions is related to the discreetness and finiteness of the Machian ensemble.Comment: Minor corrections, the version accepted by Int. J. Theor. Phy

Two-Component Fluid Membranes Near Repulsive Walls: Linearized Hydrodynamics of Equilibrium and Non-equilibrium States

We study the linearized hydrodynamics of a two-component fluid membrane near a repulsive wall, via a model which incorporates curvature- concentration coupling as well as hydrodynamic interactions. This model is a simplified version of a recently proposed one [J.-B. Manneville et al. Phys. Rev. E, 64, 021908 (2001)] for non-equilibrium force-centres embedded in fluid membranes, such as light-activated bacteriorhodopsin pumps incorporated in phospholipid (EPC) bilayers. The pump/membrane system is modeled as an impermeable, two-component bilayer fluid membrane in the presence of an ambient solvent, in which one component, representing active pumps, is described in terms of force dipoles displaced with respect to the bilayer midpoint. We first discuss the case in which such pumps are rendered inactive, computing the mode structure in the bulk as well as the modification of hydrodynamic properties by the presence of a nearby wall. We then discuss the fluctuations and mode structure in steady state of active two-component membranes near a repulsive wall. We find that proximity to the wall smoothens membrane height fluctuations in the stable regime, resulting in a logarithmic scaling of the roughness even for initially tensionless membranes. This explicitly non-equilibrium result, a consequence of the incorporation of curvature-concentration coupling in our treatment, also indicates that earlier scaling arguments which obtained an increase in the roughness of active membranes near repulsive walls may need to be reevaluated.Comment: 39 page Latex file, 3 encapsulated Postscript figure